runMode: serial
maxCount: 10000
repeat: 1
LOCheck: 0
dataset: codeTables
datafile: QECC_sample.txt
method: magmaMinWeight
ignoreTrivialCodes: 1
resume: 0
nMin: 1
nMax: 100000
iterCount: 10000
maxTime: 28800
nThreads: 1
verbose: False
maxErr: -1
GF4blockRep: 2
regroupPerm: 1
filterCircuit: 1
HL: 0
genCount: 100
offspring: 10
pMut: 2.0
sMut: 0.2
tabuLength: 0
swapPivot: 1
swapBlockorder: 0
pMutScale: 50
CCstart: -1
pySATsolver: g4
pySATbinary: lsu
addStabs: 0
permuteDEM: 1
outfile: /Users/markwebster/Dropbox/QuantumComputing/dev/codeDistance-main/examples/results/codeTables-QECC_sample.txt-magmaMinWeight-20260303_211626.143623_85062422.txt
#########################################
name	n	k	d	delta d	Time	R	T	Progress
[[3,1,1]]	3	1	1	0	1.5521780420094728	1	1	Magma V2.28-26    Tue Mar  3 2026 21:16:27 on Marks-MacBook-Air-2 [Seed = \n3305890701]\nType ? for help.  Type <Ctrl>-D to quit.\n[[3, 1]] quantum code over GF(2^2), stabilised by:\nCalculating the Weight Distribution for [3, 4] linear code, #R = 4\nNumber of threads: 1\nCalculating the Weight Distribution for [3, 2] linear code, #R = 4\nNumber of threads: 1\nDoing quick check for code being known to be MDS:\nCode is not known to be MDS\nCalculating the Weight Distribution for [3, 4] linear code, #R = 4\nNumber of threads: 1\nDoing quick check for code being known to be MDS:\nCode is not known to be MDS\nUsing the Dual\n1\n\nTotal time: 0.010 seconds, Total memory usage: 32.09MB\n
[[4,1,2]]	4	1	2	0	0.06842216599034145	1	1	Magma V2.28-26    Tue Mar  3 2026 21:16:27 on Marks-MacBook-Air-2 [Seed = \n3473009031]\nType ? for help.  Type <Ctrl>-D to quit.\n[[4, 1]] quantum code over GF(2^2), stabilised by:\nCalculating the Weight Distribution for [4, 5] linear code, #R = 4\nNumber of threads: 1\nCalculating the Weight Distribution for [4, 3] linear code, #R = 4\nNumber of threads: 1\nDoing quick check for code being known to be MDS:\nCode is not known to be MDS\nCalculating the Weight Distribution for [4, 5] linear code, #R = 4\nNumber of threads: 1\nDoing quick check for code being known to be MDS:\nCode is not known to be MDS\nUsing the Dual\n2\n\nTotal time: 0.010 seconds, Total memory usage: 32.09MB\n
[[5,1,3]]	5	1	3	0	0.0647146670089569	1	1	Magma V2.28-26    Tue Mar  3 2026 21:16:27 on Marks-MacBook-Air-2 [Seed = \n3508533145]\nType ? for help.  Type <Ctrl>-D to quit.\n[[5, 1]] quantum code over GF(2^2), stabilised by:\nCalculating the Weight Distribution for [5, 6] linear code, #R = 4\nNumber of threads: 1\nCalculating the Weight Distribution for [5, 4] linear code, #R = 4\nNumber of threads: 1\nDoing quick check for code being known to be MDS:\nCode is not known to be MDS\nCalculating the Weight Distribution for [5, 2] linear code, #R = 4\nNumber of threads: 1\nDoing quick check for code being known to be MDS:\nCode is not known to be MDS\nCalculating the Weight Distribution for [5, 6] linear code, #R = 4\nNumber of threads: 1\nDoing quick check for code being known to be MDS:\nCode is not known to be MDS\nUsing the Dual\n3\n\nTotal time: 0.010 seconds, Total memory usage: 32.09MB\n
[[6,1,3]]	6	1	3	0	0.06654470798093826	1	1	Magma V2.28-26    Tue Mar  3 2026 21:16:27 on Marks-MacBook-Air-2 [Seed = \n3675651475]\nType ? for help.  Type <Ctrl>-D to quit.\n[[6, 1]] quantum code over GF(2^2), stabilised by:\nQuantum GF(2)-Additive code over GF(4) of length 6 with 7 generators.\nLower Bound: 1, Upper Bound: 4\nConstructed 2 distinct generator matrices\nTotal Ranks:      4   4 \nRelative Ranks:   4   2 \n(4 4 4 2 )\n(4 4 4 2 )\nTime Taken: 0.00\nStarting search for low weight codewords... (reset timings)\nEnumerating using 1 generator at a time:\n     New codeword identified of weight 3, time 0.00\n     Impurity detected of weight 1, time 0.00\n     Discarding non-contributing rank 2 matrix\n     New Total Ranks:      4 \n     New Relative Ranks:   4 \n   Completed Matrix  1:  lower =  2, upper =  3. Elapsed: 0.00s\nTermination predicted with 2 generators at matrix 1\nEnumerating using 2 generators at a time:\n   Completed Matrix  1:  lower =  3, upper =  3. Elapsed: 0.00s\nComputation complete \nFinal Results: lower = 3, upper = 3,\nTotal CPU time: 0.00, real time: 0.004\n3\n\nTotal time: 0.010 seconds, Total memory usage: 32.09MB\n
[[7,1,3]]	7	1	3	0	0.08364737502415664	1	1	Magma V2.28-26    Tue Mar  3 2026 21:16:28 on Marks-MacBook-Air-2 [Seed = \n3709074322]\nType ? for help.  Type <Ctrl>-D to quit.\n[[7, 1]] quantum code over GF(2^2), stabilised by:\nQuantum GF(2)-Additive code over GF(4) of length 7 with 8 generators.\nLower Bound: 1, Upper Bound: 4\nBCHBound gives the lower bound = 3\nConstructed 2 distinct generator matrices\nTotal Ranks:      4   4 \nRelative Ranks:   4   3 \n(4 4 4 4 )\n(4 4 4 4 )\nTime Taken: 0.00\nStarting search for low weight codewords... (reset timings)\nEnumerating using 1 generator at a time:\n     New codeword identified of weight 3, time 0.00\nComputation complete \nFinal Results: lower = 3, upper = 3,\nTotal CPU time: 0.00, real time: 0.011\n3\n\nTotal time: 0.010 seconds, Total memory usage: 32.09MB\n
[[8,1,3]]	8	1	3	0	0.059326249989680946	1	1	Magma V2.28-26    Tue Mar  3 2026 21:16:28 on Marks-MacBook-Air-2 [Seed = \n2808709608]\nType ? for help.  Type <Ctrl>-D to quit.\n[[8, 1]] quantum code over GF(2^2), stabilised by:\nQuantum GF(2)-Additive code over GF(4) of length 8 with 9 generators.\nLower Bound: 1, Upper Bound: 5\nConstructed 2 distinct generator matrices\nTotal Ranks:      6   6 \nRelative Ranks:   6   2 \n(4 4 4 2 2 2 )\n(4 4 4 2 2 2 )\n     Discarding non-contributing rank 2 matrix\n     New Total Ranks:      6 \n     New Relative Ranks:   6 \nTime Taken: 0.00\nStarting search for low weight codewords... (reset timings)\nEnumerating using 1 generator at a time:\n     New codeword identified of weight 3, time 0.00\n     Impurity detected of weight 1, time 0.00\n   Completed Matrix  1:  lower =  2, upper =  3. Elapsed: 0.00s\nTermination predicted with 2 generators at matrix 1\nEnumerating using 2 generators at a time:\n   Completed Matrix  1:  lower =  3, upper =  3. Elapsed: 0.00s\nComputation complete \nFinal Results: lower = 3, upper = 3,\nTotal CPU time: 0.00, real time: 0.001\n3\n\nTotal time: 0.010 seconds, Total memory usage: 32.09MB\n
[[9,1,3]]	9	1	3	0	0.05939095900976099	1	1	Magma V2.28-26    Tue Mar  3 2026 21:16:28 on Marks-MacBook-Air-2 [Seed = \n2842136550]\nType ? for help.  Type <Ctrl>-D to quit.\n[[9, 1]] quantum code over GF(2^2), stabilised by:\nQuantum GF(2)-Additive code over GF(4) of length 9 with 10 generators.\nLower Bound: 1, Upper Bound: 5\nConstructed 2 distinct generator matrices\nTotal Ranks:      7   7 \nRelative Ranks:   7   2 \n(4 4 4 2 2 2 2 )\n(4 4 4 2 2 2 2 )\n     Discarding non-contributing rank 2 matrix\n     New Total Ranks:      7 \n     New Relative Ranks:   7 \nTime Taken: 0.00\nStarting search for low weight codewords... (reset timings)\nEnumerating using 1 generator at a time:\n     New codeword identified of weight 3, time 0.00\n     Impurity detected of weight 1, time 0.00\n   Completed Matrix  1:  lower =  2, upper =  3. Elapsed: 0.00s\nTermination predicted with 2 generators at matrix 1\nEnumerating using 2 generators at a time:\n   Completed Matrix  1:  lower =  3, upper =  3. Elapsed: 0.00s\nComputation complete \nFinal Results: lower = 3, upper = 3,\nTotal CPU time: 0.00, real time: 0.001\n3\n\nTotal time: 0.010 seconds, Total memory usage: 32.09MB\n
[[10,1,4]]	10	1	4	0	0.06515812498400919	1	1	Magma V2.28-26    Tue Mar  3 2026 21:16:28 on Marks-MacBook-Air-2 [Seed = \n3011352060]\nType ? for help.  Type <Ctrl>-D to quit.\n[[10, 1]] quantum code over GF(2^2), stabilised by:\nQuantum GF(2)-Additive code over GF(4) of length 10 with 11 generators.\nLower Bound: 1, Upper Bound: 6\nConstructed 2 distinct generator matrices\nTotal Ranks:      6   6 \nRelative Ranks:   6   4 \n(4 4 4 4 4 2 )\n(4 4 4 4 2 4 )\nTime Taken: 0.00\nStarting search for low weight codewords... (reset timings)\nEnumerating using 1 generator at a time:\n     New codeword identified of weight 5, time 0.00\n     New codeword identified of weight 4, time 0.00\n   Completed Matrix  1:  lower =  2, upper =  4. Elapsed: 0.00s\n   Completed Matrix  2:  lower =  2, upper =  4. Elapsed: 0.00s\nTermination predicted with 2 generators at matrix 2\nEnumerating using 2 generators at a time:\n   Completed Matrix  1:  lower =  3, upper =  4. Elapsed: 0.00s\n   Completed Matrix  2:  lower =  4, upper =  4. Elapsed: 0.00s\nComputation complete \nFinal Results: lower = 4, upper = 4,\nTotal CPU time: 0.00, real time: 0.001\n4\n\nTotal time: 0.010 seconds, Total memory usage: 32.09MB\n
[[11,1,5]]	11	1	5	0	0.05914937501074746	1	1	Magma V2.28-26    Tue Mar  3 2026 21:16:28 on Marks-MacBook-Air-2 [Seed = \n3044774906]\nType ? for help.  Type <Ctrl>-D to quit.\n[[11, 1]] quantum code over GF(2^2), stabilised by:\nQuantum GF(2)-Additive code over GF(4) of length 11 with 12 generators.\nLower Bound: 1, Upper Bound: 6\nConstructed 2 distinct generator matrices\nTotal Ranks:      6   6 \nRelative Ranks:   6   5 \n(4 4 4 4 4 4 )\n(4 4 4 4 4 4 )\nTime Taken: 0.00\nStarting search for low weight codewords... (reset timings)\nEnumerating using 1 generator at a time:\n     New codeword identified of weight 5, time 0.00\n   Completed Matrix  1:  lower =  2, upper =  5. Elapsed: 0.00s\n   Completed Matrix  2:  lower =  3, upper =  5. Elapsed: 0.00s\nTermination predicted with 2 generators at matrix 2\nEnumerating using 2 generators at a time:\n   Completed Matrix  1:  lower =  4, upper =  5. Elapsed: 0.00s\n   Completed Matrix  2:  lower =  5, upper =  5. Elapsed: 0.00s\nComputation complete \nFinal Results: lower = 5, upper = 5,\nTotal CPU time: 0.00, real time: 0.001\n5\n\nTotal time: 0.010 seconds, Total memory usage: 32.09MB\n
[[12,6,3]]	12	6	3	0	0.06306324998149648	1	1	Magma V2.28-26    Tue Mar  3 2026 21:16:28 on Marks-MacBook-Air-2 [Seed = \n3211893232]\nType ? for help.  Type <Ctrl>-D to quit.\n[[12, 6]] quantum code over GF(2^2), stabilised by:\nQuantum GF(2)-Additive code over GF(4) of length 12 with 18 generators.\nLower Bound: 1, Upper Bound: 4\nConstructed 2 distinct generator matrices\nTotal Ranks:      9   9 \nRelative Ranks:   9   3 \n(4 4 4 4 4 4 4 4 4 )\n(4 4 4 4 4 4 4 4 4 )\n     Discarding non-contributing rank 3 matrix\n     New Total Ranks:      9 \n     New Relative Ranks:   9 \nTime Taken: 0.00\nStarting search for low weight codewords... (reset timings)\nEnumerating using 1 generator at a time:\n     New codeword identified of weight 3, time 0.00\n   Completed Matrix  1:  lower =  2, upper =  3. Elapsed: 0.00s\nTermination predicted with 2 generators at matrix 1\nEnumerating using 2 generators at a time:\n   Completed Matrix  1:  lower =  3, upper =  3. Elapsed: 0.00s\nComputation complete \nFinal Results: lower = 3, upper = 3,\nTotal CPU time: 0.00, real time: 0.001\n3\n\nTotal time: 0.019 seconds, Total memory usage: 32.09MB\n
[[13,6,3]]	13	6	3	0	0.06289683302748017	1	1	Magma V2.28-26    Tue Mar  3 2026 21:16:28 on Marks-MacBook-Air-2 [Seed = \n2169481166]\nType ? for help.  Type <Ctrl>-D to quit.\n[[13, 6]] quantum code over GF(2^2), stabilised by:\nQuantum GF(2)-Additive code over GF(4) of length 13 with 19 generators.\nLower Bound: 1, Upper Bound: 5\nConstructed 2 distinct generator matrices\nTotal Ranks:     10  10 \nRelative Ranks:  10   3 \n(4 4 4 4 4 4 4 4 4 2 )\n(4 4 4 4 4 4 4 4 4 2 )\n     Discarding non-contributing rank 3 matrix\n     New Total Ranks:     10 \n     New Relative Ranks:  10 \nTime Taken: 0.00\nStarting search for low weight codewords... (reset timings)\nEnumerating using 1 generator at a time:\n     New codeword identified of weight 3, time 0.00\n     Impurity detected of weight 1, time 0.00\n   Completed Matrix  1:  lower =  2, upper =  3. Elapsed: 0.00s\nTermination predicted with 2 generators at matrix 1\nEnumerating using 2 generators at a time:\n   Completed Matrix  1:  lower =  3, upper =  3. Elapsed: 0.00s\nComputation complete \nFinal Results: lower = 3, upper = 3,\nTotal CPU time: 0.00, real time: 0.002\n3\n\nTotal time: 0.010 seconds, Total memory usage: 32.09MB\n
[[14,2,5]]	14	2	5	0	0.06399929197505116	1	1	Magma V2.28-26    Tue Mar  3 2026 21:16:28 on Marks-MacBook-Air-2 [Seed = \n2336599492]\nType ? for help.  Type <Ctrl>-D to quit.\n[[14, 2]] quantum code over GF(2^2), stabilised by:\nQuantum GF(2)-Additive code over GF(4) of length 14 with 16 generators.\nLower Bound: 1, Upper Bound: 7\nConstructed 2 distinct generator matrices\nTotal Ranks:      8   8 \nRelative Ranks:   8   6 \n(4 4 4 4 4 4 4 4 )\n(4 4 4 4 4 4 4 4 )\nTime Taken: 0.00\nStarting search for low weight codewords... (reset timings)\nEnumerating using 1 generator at a time:\n     New codeword identified of weight 5, time 0.00\n   Completed Matrix  1:  lower =  2, upper =  5. Elapsed: 0.00s\n   Completed Matrix  2:  lower =  2, upper =  5. Elapsed: 0.00s\nTermination predicted with 3 generators at matrix 1\nEnumerating using 2 generators at a time:\n   Completed Matrix  1:  lower =  3, upper =  5. Elapsed: 0.00s\n   Completed Matrix  2:  lower =  4, upper =  5. Elapsed: 0.00s\nTermination predicted with 3 generators at matrix 1\nEnumerating using 3 generators at a time:\n   Completed Matrix  1:  lower =  5, upper =  5. Elapsed: 0.00s\nComputation complete \nFinal Results: lower = 5, upper = 5,\nTotal CPU time: 0.00, real time: 0.001\n5\n\nTotal time: 0.010 seconds, Total memory usage: 32.09MB\n
[[15,2,5]]	15	2	5	0	0.07951150002190843	1	1	Magma V2.28-26    Tue Mar  3 2026 21:16:28 on Marks-MacBook-Air-2 [Seed = \n2370022338]\nType ? for help.  Type <Ctrl>-D to quit.\n[[15, 2]] quantum code over GF(2^2), stabilised by:\nQuantum GF(2)-Additive code over GF(4) of length 15 with 17 generators.\nLower Bound: 1, Upper Bound: 8\nConstructed 2 distinct generator matrices\nTotal Ranks:      9   9 \nRelative Ranks:   9   6 \n(4 4 4 4 4 4 4 4 2 )\n(4 4 4 4 4 4 4 4 2 )\nTime Taken: 0.00\nStarting search for low weight codewords... (reset timings)\nEnumerating using 1 generator at a time:\n     New codeword identified of weight 5, time 0.00\n     Impurity detected of weight 1, time 0.00\n   Completed Matrix  1:  lower =  2, upper =  5. Elapsed: 0.00s\n   Completed Matrix  2:  lower =  2, upper =  5. Elapsed: 0.00s\nTermination predicted with 3 generators at matrix 2\nEnumerating using 2 generators at a time:\n   Completed Matrix  1:  lower =  3, upper =  5. Elapsed: 0.00s\n   Completed Matrix  2:  lower =  3, upper =  5. Elapsed: 0.00s\nTermination predicted with 3 generators at matrix 2\nEnumerating using 3 generators at a time:\n   Completed Matrix  1:  lower =  4, upper =  5. Elapsed: 0.00s\n   Completed Matrix  2:  lower =  5, upper =  5. Elapsed: 0.00s\nComputation complete \nFinal Results: lower = 5, upper = 5,\nTotal CPU time: 0.00, real time: 0.002\n5\n\nTotal time: 0.010 seconds, Total memory usage: 32.09MB\n
[[16,1,6]]	16	1	6	0	0.06650320798507892	1	1	Magma V2.28-26    Tue Mar  3 2026 21:16:28 on Marks-MacBook-Air-2 [Seed = \n2539237848]\nType ? for help.  Type <Ctrl>-D to quit.\n[[16, 1]] quantum code over GF(2^2), stabilised by:\nQuantum GF(2)-Additive code over GF(4) of length 16 with 17 generators.\nLower Bound: 1, Upper Bound: 9\nConstructed 2 distinct generator matrices\nTotal Ranks:      9   9 \nRelative Ranks:   9   7 \n(4 4 4 4 4 4 4 4 2 )\n(4 4 4 4 4 4 4 4 2 )\nTime Taken: 0.00\nStarting search for low weight codewords... (reset timings)\nEnumerating using 1 generator at a time:\n     New codeword identified of weight 8, time 0.00\n     New codeword identified of weight 7, time 0.00\n     New codeword identified of weight 6, time 0.00\n   Completed Matrix  1:  lower =  2, upper =  6. Elapsed: 0.00s\n   Completed Matrix  2:  lower =  2, upper =  6. Elapsed: 0.00s\nTermination predicted with 3 generators at matrix 2\nEnumerating using 2 generators at a time:\n   Completed Matrix  1:  lower =  3, upper =  6. Elapsed: 0.00s\n   Completed Matrix  2:  lower =  4, upper =  6. Elapsed: 0.00s\nTermination predicted with 3 generators at matrix 2\nEnumerating using 3 generators at a time:\n   Completed Matrix  1:  lower =  5, upper =  6. Elapsed: 0.00s\n   Completed Matrix  2:  lower =  6, upper =  6. Elapsed: 0.00s\nComputation complete \nFinal Results: lower = 6, upper = 6,\nTotal CPU time: 0.00, real time: 0.002\n6\n\nTotal time: 0.010 seconds, Total memory usage: 32.09MB\n
[[17,3,5]]	17	3	5	0	0.06581158301560208	1	1	Magma V2.28-26    Tue Mar  3 2026 21:16:28 on Marks-MacBook-Air-2 [Seed = \n2572664790]\nType ? for help.  Type <Ctrl>-D to quit.\n[[17, 3]] quantum code over GF(2^2), stabilised by:\nQuantum GF(2)-Additive code over GF(4) of length 17 with 20 generators.\nLower Bound: 1, Upper Bound: 8\nConstructed 2 distinct generator matrices\nTotal Ranks:     11  11 \nRelative Ranks:  11   6 \n(4 4 4 4 4 4 4 4 4 2 2 )\n(4 4 4 4 4 4 4 4 4 2 2 )\nTime Taken: 0.00\nStarting search for low weight codewords... (reset timings)\nEnumerating using 1 generator at a time:\n     New codeword identified of weight 6, time 0.00\n     New codeword identified of weight 5, time 0.00\n     Impurity detected of weight 1, time 0.00\n     Discarding non-contributing rank 6 matrix\n     New Total Ranks:     11 \n     New Relative Ranks:  11 \n   Completed Matrix  1:  lower =  2, upper =  5. Elapsed: 0.00s\nTermination predicted with 4 generators at matrix 1\nEnumerating using 2 generators at a time:\n   Completed Matrix  1:  lower =  3, upper =  5. Elapsed: 0.00s\nTermination predicted with 4 generators at matrix 1\nEnumerating using 3 generators at a time:\n   Completed Matrix  1:  lower =  4, upper =  5. Elapsed: 0.00s\nTermination predicted with 4 generators at matrix 1\nEnumerating using 4 generators at a time:\n   Completed Matrix  1:  lower =  5, upper =  5. Elapsed: 0.00s\nComputation complete \nFinal Results: lower = 5, upper = 5,\nTotal CPU time: 0.00, real time: 0.002\n5\n\nTotal time: 0.010 seconds, Total memory usage: 32.09MB\n
[[18,5,5]]	18	5	5	0	0.06592929200269282	1	1	Magma V2.28-26    Tue Mar  3 2026 21:16:28 on Marks-MacBook-Air-2 [Seed = \n1672299820]\nType ? for help.  Type <Ctrl>-D to quit.\n[[18, 5]] quantum code over GF(2^2), stabilised by:\nQuantum GF(2)-Additive code over GF(4) of length 18 with 23 generators.\nLower Bound: 1, Upper Bound: 8\nConstructed 2 distinct generator matrices\nTotal Ranks:     12  12 \nRelative Ranks:  12   6 \n(4 4 4 4 4 4 4 4 4 4 2 4 )\n(4 4 4 4 4 4 4 4 4 4 4 2 )\nTime Taken: 0.00\nStarting search for low weight codewords... (reset timings)\nEnumerating using 1 generator at a time:\n     New codeword identified of weight 6, time 0.00\n     New codeword identified of weight 5, time 0.00\n     Discarding non-contributing rank 6 matrix\n     New Total Ranks:     12 \n     New Relative Ranks:  12 \n   Completed Matrix  1:  lower =  2, upper =  5. Elapsed: 0.00s\nTermination predicted with 4 generators at matrix 1\nEnumerating using 2 generators at a time:\n   Completed Matrix  1:  lower =  3, upper =  5. Elapsed: 0.00s\nTermination predicted with 4 generators at matrix 1\nEnumerating using 3 generators at a time:\n   Completed Matrix  1:  lower =  4, upper =  5. Elapsed: 0.00s\nTermination predicted with 4 generators at matrix 1\nEnumerating using 4 generators at a time:\n   Completed Matrix  1:  lower =  5, upper =  5. Elapsed: 0.00s\nComputation complete \nFinal Results: lower = 5, upper = 5,\nTotal CPU time: 0.00, real time: 0.002\n5\n\nTotal time: 0.010 seconds, Total memory usage: 32.09MB\n
[[19,5,5]]	19	5	5	0	0.06660954197286628	1	1	Magma V2.28-26    Tue Mar  3 2026 21:16:28 on Marks-MacBook-Air-2 [Seed = \n1705722666]\nType ? for help.  Type <Ctrl>-D to quit.\n[[19, 5]] quantum code over GF(2^2), stabilised by:\nQuantum GF(2)-Additive code over GF(4) of length 19 with 24 generators.\nLower Bound: 1, Upper Bound: 8\nConstructed 2 distinct generator matrices\nTotal Ranks:     13  13 \nRelative Ranks:  13   6 \n(4 4 4 4 4 4 4 4 4 4 2 4 2 )\n(4 4 4 4 4 4 4 4 4 4 4 2 2 )\n     Discarding non-contributing rank 6 matrix\n     New Total Ranks:     13 \n     New Relative Ranks:  13 \nTime Taken: 0.00\nStarting search for low weight codewords... (reset timings)\nEnumerating using 1 generator at a time:\n     New codeword identified of weight 6, time 0.00\n     New codeword identified of weight 5, time 0.00\n     Impurity detected of weight 1, time 0.00\n   Completed Matrix  1:  lower =  2, upper =  5. Elapsed: 0.00s\nTermination predicted with 4 generators at matrix 1\nEnumerating using 2 generators at a time:\n   Completed Matrix  1:  lower =  3, upper =  5. Elapsed: 0.00s\nTermination predicted with 4 generators at matrix 1\nEnumerating using 3 generators at a time:\n   Completed Matrix  1:  lower =  4, upper =  5. Elapsed: 0.00s\nTermination predicted with 4 generators at matrix 1\nEnumerating using 4 generators at a time:\n   Completed Matrix  1:  lower =  5, upper =  5. Elapsed: 0.00s\nComputation complete \nFinal Results: lower = 5, upper = 5,\nTotal CPU time: 0.00, real time: 0.002\n5\n\nTotal time: 0.010 seconds, Total memory usage: 32.09MB\n
[[20,3,6]]	20	3	6	0	0.06576670802314766	1	1	Magma V2.28-26    Tue Mar  3 2026 21:16:28 on Marks-MacBook-Air-2 [Seed = \n1872840992]\nType ? for help.  Type <Ctrl>-D to quit.\n[[20, 3]] quantum code over GF(2^2), stabilised by:\nQuantum GF(2)-Additive code over GF(4) of length 20 with 23 generators.\nLower Bound: 1, Upper Bound: 10\nConstructed 2 distinct generator matrices\nTotal Ranks:     12  12 \nRelative Ranks:  12   8 \n(4 4 4 4 4 4 4 4 4 4 4 2 )\n(4 4 4 4 4 4 4 4 4 4 4 2 )\nTime Taken: 0.00\nStarting search for low weight codewords... (reset timings)\nEnumerating using 1 generator at a time:\n     New codeword identified of weight 8, time 0.00\n     New codeword identified of weight 7, time 0.00\n   Completed Matrix  1:  lower =  2, upper =  7. Elapsed: 0.00s\n     New codeword identified of weight 6, time 0.00\n   Completed Matrix  2:  lower =  2, upper =  6. Elapsed: 0.00s\nTermination predicted with 4 generators at matrix 2\nEnumerating using 2 generators at a time:\n   Completed Matrix  1:  lower =  3, upper =  6. Elapsed: 0.00s\n   Completed Matrix  2:  lower =  3, upper =  6. Elapsed: 0.00s\nTermination predicted with 4 generators at matrix 2\nEnumerating using 3 generators at a time:\n   Completed Matrix  1:  lower =  4, upper =  6. Elapsed: 0.00s\n   Completed Matrix  2:  lower =  4, upper =  6. Elapsed: 0.00s\nTermination predicted with 4 generators at matrix 2\nEnumerating using 4 generators at a time:\n   Completed Matrix  1:  lower =  5, upper =  6. Elapsed: 0.00s\n   Completed Matrix  2:  lower =  6, upper =  6. Elapsed: 0.00s\nComputation complete \nFinal Results: lower = 6, upper = 6,\nTotal CPU time: 0.00, real time: 0.002\n6\n\nTotal time: 0.010 seconds, Total memory usage: 32.09MB\n
[[21,3,6]]	21	3	6	0	0.06296745798317716	1	1	Magma V2.28-26    Tue Mar  3 2026 21:16:28 on Marks-MacBook-Air-2 [Seed = \n1908365118]\nType ? for help.  Type <Ctrl>-D to quit.\n[[21, 3]] quantum code over GF(2^2), stabilised by:\nQuantum GF(2)-Additive code over GF(4) of length 21 with 24 generators.\nLower Bound: 1, Upper Bound: 10\nConstructed 2 distinct generator matrices\nTotal Ranks:     13  13 \nRelative Ranks:  13   8 \n(4 4 4 4 4 4 4 4 4 4 4 2 2 )\n(4 4 4 4 4 4 4 4 4 4 4 2 2 )\nTime Taken: 0.00\nStarting search for low weight codewords... (reset timings)\nEnumerating using 1 generator at a time:\n     New codeword identified of weight 8, time 0.00\n     New codeword identified of weight 7, time 0.00\n     Impurity detected of weight 1, time 0.00\n   Completed Matrix  1:  lower =  2, upper =  7. Elapsed: 0.00s\n     New codeword identified of weight 6, time 0.00\n     Discarding non-contributing rank 8 matrix\n     New Total Ranks:     13 \n     New Relative Ranks:  13 \n   Completed Matrix  2:  lower =  2, upper =  6. Elapsed: 0.00s\nTermination predicted with 5 generators at matrix 1\nEnumerating using 2 generators at a time:\n   Completed Matrix  1:  lower =  3, upper =  6. Elapsed: 0.00s\nTermination predicted with 5 generators at matrix 1\nEnumerating using 3 generators at a time:\n   Completed Matrix  1:  lower =  4, upper =  6. Elapsed: 0.00s\nTermination predicted with 5 generators at matrix 1\nEnumerating using 4 generators at a time:\n   Completed Matrix  1:  lower =  5, upper =  6. Elapsed: 0.00s\nTermination predicted with 5 generators at matrix 1\nEnumerating using 5 generators at a time:\n   Completed Matrix  1:  lower =  6, upper =  6. Elapsed: 0.00s\nComputation complete \nFinal Results: lower = 6, upper = 6,\nTotal CPU time: 0.00, real time: 0.003\n6\n\nTotal time: 0.010 seconds, Total memory usage: 32.09MB\n
[[22,7,5]]	22	7	5	0	0.06370520900236443	1	1	Magma V2.28-26    Tue Mar  3 2026 21:16:29 on Marks-MacBook-Air-2 [Seed = \n2075483445]\nType ? for help.  Type <Ctrl>-D to quit.\n[[22, 7]] quantum code over GF(2^2), stabilised by:\nQuantum GF(2)-Additive code over GF(4) of length 22 with 29 generators.\nLower Bound: 1, Upper Bound: 9\nConstructed 2 distinct generator matrices\nTotal Ranks:     15  15 \nRelative Ranks:  15   7 \n(4 4 4 4 4 4 4 4 4 4 4 4 4 4 2 )\n(4 4 4 4 4 4 4 4 4 4 4 4 4 4 2 )\n     Discarding non-contributing rank 7 matrix\n     New Total Ranks:     15 \n     New Relative Ranks:  15 \nTime Taken: 0.00\nStarting search for low weight codewords... (reset timings)\nEnumerating using 1 generator at a time:\n     New codeword identified of weight 5, time 0.00\n     Impurity detected of weight 1, time 0.00\n   Completed Matrix  1:  lower =  2, upper =  5. Elapsed: 0.00s\nTermination predicted with 4 generators at matrix 1\nEnumerating using 2 generators at a time:\n   Completed Matrix  1:  lower =  3, upper =  5. Elapsed: 0.00s\nTermination predicted with 4 generators at matrix 1\nEnumerating using 3 generators at a time:\n   Completed Matrix  1:  lower =  4, upper =  5. Elapsed: 0.00s\nTermination predicted with 4 generators at matrix 1\nEnumerating using 4 generators at a time:\n   Completed Matrix  1:  lower =  5, upper =  5. Elapsed: 0.00s\nComputation complete \nFinal Results: lower = 5, upper = 5,\nTotal CPU time: 0.00, real time: 0.003\n5\n\nTotal time: 0.010 seconds, Total memory usage: 32.09MB\n
[[23,2,7]]	23	2	7	0	0.06765220800298266	1	1	Magma V2.28-26    Tue Mar  3 2026 21:16:29 on Marks-MacBook-Air-2 [Seed = \n2108906291]\nType ? for help.  Type <Ctrl>-D to quit.\n[[23, 2]] quantum code over GF(2^2), stabilised by:\nQuantum GF(2)-Additive code over GF(4) of length 23 with 25 generators.\nLower Bound: 1, Upper Bound: 12\nConstructed 2 distinct generator matrices\nTotal Ranks:     13  13 \nRelative Ranks:  13  10 \n(4 4 4 4 4 4 4 4 4 4 4 4 2 )\n(4 4 4 4 4 4 4 4 4 4 4 4 2 )\nTime Taken: 0.00\nStarting search for low weight codewords... (reset timings)\nEnumerating using 1 generator at a time:\n     New codeword identified of weight 11, time 0.00\n     New codeword identified of weight 9, time 0.00\n     New codeword identified of weight 8, time 0.00\n     New codeword identified of weight 7, time 0.00\n   Completed Matrix  1:  lower =  2, upper =  7. Elapsed: 0.00s\n   Completed Matrix  2:  lower =  2, upper =  7. Elapsed: 0.00s\nTermination predicted with 4 generators at matrix 2\nEnumerating using 2 generators at a time:\n   Completed Matrix  1:  lower =  3, upper =  7. Elapsed: 0.00s\n   Completed Matrix  2:  lower =  3, upper =  7. Elapsed: 0.00s\nTermination predicted with 4 generators at matrix 2\nEnumerating using 3 generators at a time:\n   Completed Matrix  1:  lower =  4, upper =  7. Elapsed: 0.00s\n   Completed Matrix  2:  lower =  5, upper =  7. Elapsed: 0.00s\nTermination predicted with 4 generators at matrix 2\nEnumerating using 4 generators at a time:\n   Completed Matrix  1:  lower =  6, upper =  7. Elapsed: 0.00s\n   Completed Matrix  2:  lower =  7, upper =  7. Elapsed: 0.00s\nComputation complete \nFinal Results: lower = 7, upper = 7,\nTotal CPU time: 0.00, real time: 0.002\n7\n\nTotal time: 0.010 seconds, Total memory usage: 32.09MB\n
[[24,8,5]]	24	8	5	0	0.07564662498771213	1	1	Magma V2.28-26    Tue Mar  3 2026 21:16:29 on Marks-MacBook-Air-2 [Seed = \n1200185609]\nType ? for help.  Type <Ctrl>-D to quit.\n[[24, 8]] quantum code over GF(2^2), stabilised by:\nQuantum GF(2)-Additive code over GF(4) of length 24 with 32 generators.\nLower Bound: 1, Upper Bound: 9\nConstructed 2 distinct generator matrices\nTotal Ranks:     16  16 \nRelative Ranks:  16   8 \n(4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 )\n(4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 )\n     Discarding non-contributing rank 8 matrix\n     New Total Ranks:     16 \n     New Relative Ranks:  16 \nTime Taken: 0.00\nStarting search for low weight codewords... (reset timings)\nEnumerating using 1 generator at a time:\n     New codeword identified of weight 7, time 0.00\n   Completed Matrix  1:  lower =  2, upper =  7. Elapsed: 0.00s\nTermination predicted with 6 generators at matrix 1\nEnumerating using 2 generators at a time:\n     New codeword identified of weight 6, time 0.00\n     New codeword identified of weight 5, time 0.00\n   Completed Matrix  1:  lower =  3, upper =  5. Elapsed: 0.00s\nTermination predicted with 4 generators at matrix 1\nEnumerating using 3 generators at a time:\n   Completed Matrix  1:  lower =  4, upper =  5. Elapsed: 0.00s\nTermination predicted with 4 generators at matrix 1\nEnumerating using 4 generators at a time:\n   Completed Matrix  1:  lower =  5, upper =  5. Elapsed: 0.00s\nComputation complete \nFinal Results: lower = 5, upper = 5,\nTotal CPU time: 0.00, real time: 0.004\n5\n\nTotal time: 0.010 seconds, Total memory usage: 32.09MB\n
[[25,8,5]]	25	8	5	0	0.07840116700390354	1	1	Magma V2.28-26    Tue Mar  3 2026 21:16:29 on Marks-MacBook-Air-2 [Seed = \n1333881089]\nType ? for help.  Type <Ctrl>-D to quit.\n[[25, 8]] quantum code over GF(2^2), stabilised by:\nQuantum GF(2)-Additive code over GF(4) of length 25 with 33 generators.\nLower Bound: 1, Upper Bound: 10\nConstructed 2 distinct generator matrices\nTotal Ranks:     17  17 \nRelative Ranks:  17   8 \n(4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2 )\n(4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2 )\n     Discarding non-contributing rank 8 matrix\n     New Total Ranks:     17 \n     New Relative Ranks:  17 \nTime Taken: 0.00\nStarting search for low weight codewords... (reset timings)\nEnumerating using 1 generator at a time:\n     New codeword identified of weight 7, time 0.00\n     Impurity detected of weight 1, time 0.00\n   Completed Matrix  1:  lower =  2, upper =  7. Elapsed: 0.00s\nTermination predicted with 6 generators at matrix 1\nEnumerating using 2 generators at a time:\n     New codeword identified of weight 6, time 0.00\n     New codeword identified of weight 5, time 0.00\n   Completed Matrix  1:  lower =  3, upper =  5. Elapsed: 0.00s\nTermination predicted with 4 generators at matrix 1\nEnumerating using 3 generators at a time:\n   Completed Matrix  1:  lower =  4, upper =  5. Elapsed: 0.00s\nTermination predicted with 4 generators at matrix 1\nEnumerating using 4 generators at a time:\n   Completed Matrix  1:  lower =  5, upper =  5. Elapsed: 0.00s\nComputation complete \nFinal Results: lower = 5, upper = 5,\nTotal CPU time: 0.00, real time: 0.003\n5\n\nTotal time: 0.010 seconds, Total memory usage: 32.09MB\n
[[26,6,6]]	26	6	6	0	0.06888233299832791	1	1	Magma V2.28-26    Tue Mar  3 2026 21:16:29 on Marks-MacBook-Air-2 [Seed = \n1369405215]\nType ? for help.  Type <Ctrl>-D to quit.\n[[26, 6]] quantum code over GF(2^2), stabilised by:\nQuantum GF(2)-Additive code over GF(4) of length 26 with 32 generators.\nLower Bound: 1, Upper Bound: 11\nConstructed 2 distinct generator matrices\nTotal Ranks:     17  17 \nRelative Ranks:  17   9 \n(4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2 2 )\n(4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2 2 )\nTime Taken: 0.00\nStarting search for low weight codewords... (reset timings)\nEnumerating using 1 generator at a time:\n     New codeword identified of weight 9, time 0.00\n     New codeword identified of weight 8, time 0.00\n     New codeword identified of weight 7, time 0.00\n     New codeword identified of weight 6, time 0.00\n     Impurity detected of weight 1, time 0.00\n     Discarding non-contributing rank 9 matrix\n     New Total Ranks:     17 \n     New Relative Ranks:  17 \n   Completed Matrix  1:  lower =  2, upper =  6. Elapsed: 0.00s\nTermination predicted with 5 generators at matrix 1\nEnumerating using 2 generators at a time:\n   Completed Matrix  1:  lower =  3, upper =  6. Elapsed: 0.00s\nTermination predicted with 5 generators at matrix 1\nEnumerating using 3 generators at a time:\n   Completed Matrix  1:  lower =  4, upper =  6. Elapsed: 0.00s\nTermination predicted with 5 generators at matrix 1\nEnumerating using 4 generators at a time:\n   Completed Matrix  1:  lower =  5, upper =  6. Elapsed: 0.00s\nTermination predicted with 5 generators at matrix 1\nEnumerating using 5 generators at a time:\n   Completed Matrix  1:  lower =  6, upper =  6. Elapsed: 0.00s\nComputation complete \nFinal Results: lower = 6, upper = 6,\nTotal CPU time: 0.00, real time: 0.009\n6\n\nTotal time: 0.019 seconds, Total memory usage: 32.09MB\n
[[27,6,6]]	27	6	6	0	0.08603579201735556	1	1	Magma V2.28-26    Tue Mar  3 2026 21:16:29 on Marks-MacBook-Air-2 [Seed = \n1536523541]\nType ? for help.  Type <Ctrl>-D to quit.\n[[27, 6]] quantum code over GF(2^2), stabilised by:\nQuantum GF(2)-Additive code over GF(4) of length 27 with 33 generators.\nLower Bound: 1, Upper Bound: 12\nConstructed 2 distinct generator matrices\nTotal Ranks:     18  18 \nRelative Ranks:  18   9 \n(4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2 2 2 )\n(4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2 2 2 )\nTime Taken: 0.00\nStarting search for low weight codewords... (reset timings)\nEnumerating using 1 generator at a time:\n     New codeword identified of weight 9, time 0.00\n     New codeword identified of weight 8, time 0.00\n     New codeword identified of weight 7, time 0.00\n     New codeword identified of weight 6, time 0.00\n     Impurity detected of weight 1, time 0.00\n     Discarding non-contributing rank 9 matrix\n     New Total Ranks:     18 \n     New Relative Ranks:  18 \n   Completed Matrix  1:  lower =  2, upper =  6. Elapsed: 0.00s\nTermination predicted with 5 generators at matrix 1\nEnumerating using 2 generators at a time:\n   Completed Matrix  1:  lower =  3, upper =  6. Elapsed: 0.00s\nTermination predicted with 5 generators at matrix 1\nEnumerating using 3 generators at a time:\n   Completed Matrix  1:  lower =  4, upper =  6. Elapsed: 0.00s\nTermination predicted with 5 generators at matrix 1\nEnumerating using 4 generators at a time:\n   Completed Matrix  1:  lower =  5, upper =  6. Elapsed: 0.00s\nTermination predicted with 5 generators at matrix 1\nEnumerating using 5 generators at a time:\n   Completed Matrix  1:  lower =  6, upper =  6. Elapsed: 0.00s\nComputation complete \nFinal Results: lower = 6, upper = 6,\nTotal CPU time: 0.00, real time: 0.010\n6\n\nTotal time: 0.019 seconds, Total memory usage: 32.09MB\n
[[28,6,6]]	28	6	6	0	0.06968708298518322	1	1	Magma V2.28-26    Tue Mar  3 2026 21:16:29 on Marks-MacBook-Air-2 [Seed = \n1569946387]\nType ? for help.  Type <Ctrl>-D to quit.\n[[28, 6]] quantum code over GF(2^2), stabilised by:\nQuantum GF(2)-Additive code over GF(4) of length 28 with 34 generators.\nLower Bound: 1, Upper Bound: 12\nConstructed 2 distinct generator matrices\nTotal Ranks:     19  19 \nRelative Ranks:  19   9 \n(4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2 2 2 2 )\n(4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2 2 2 2 )\nTime Taken: 0.00\nStarting search for low weight codewords... (reset timings)\nEnumerating using 1 generator at a time:\n     New codeword identified of weight 9, time 0.00\n     New codeword identified of weight 8, time 0.00\n     New codeword identified of weight 7, time 0.00\n     New codeword identified of weight 6, time 0.00\n     Impurity detected of weight 1, time 0.00\n     Discarding non-contributing rank 9 matrix\n     New Total Ranks:     19 \n     New Relative Ranks:  19 \n   Completed Matrix  1:  lower =  2, upper =  6. Elapsed: 0.00s\nTermination predicted with 5 generators at matrix 1\nEnumerating using 2 generators at a time:\n   Completed Matrix  1:  lower =  3, upper =  6. Elapsed: 0.00s\nTermination predicted with 5 generators at matrix 1\nEnumerating using 3 generators at a time:\n   Completed Matrix  1:  lower =  4, upper =  6. Elapsed: 0.00s\nTermination predicted with 5 generators at matrix 1\nEnumerating using 4 generators at a time:\n   Completed Matrix  1:  lower =  5, upper =  6. Elapsed: 0.00s\nTermination predicted with 5 generators at matrix 1\nEnumerating using 5 generators at a time:\n   Completed Matrix  1:  lower =  6, upper =  6. Elapsed: 0.00s\nComputation complete \nFinal Results: lower = 6, upper = 6,\nTotal CPU time: 0.00, real time: 0.011\n6\n\nTotal time: 0.019 seconds, Total memory usage: 32.09MB\n
[[29,6,7]]	29	6	7	0	0.13442583300638944	1	1	Magma V2.28-26    Tue Mar  3 2026 21:16:29 on Marks-MacBook-Air-2 [Seed = \n669581673]\nType ? for help.  Type <Ctrl>-D to quit.\n[[29, 6]] quantum code over GF(2^2), stabilised by:\nQuantum GF(2)-Additive code over GF(4) of length 29 with 35 generators.\nLower Bound: 1, Upper Bound: 13\nConstructed 2 distinct generator matrices\nTotal Ranks:     18  18 \nRelative Ranks:  18  11 \n(4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2 )\n(4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2 )\nTime Taken: 0.00\nStarting search for low weight codewords... (reset timings)\nEnumerating using 1 generator at a time:\n     New codeword identified of weight 11, time 0.00\n     New codeword identified of weight 10, time 0.00\n     New codeword identified of weight 9, time 0.00\n     New codeword identified of weight 8, time 0.00\n     New codeword identified of weight 7, time 0.00\n     Discarding non-contributing rank 11 matrix\n     New Total Ranks:     18 \n     New Relative Ranks:  18 \n   Completed Matrix  1:  lower =  2, upper =  7. Elapsed: 0.00s\nTermination predicted with 6 generators at matrix 1\nEnumerating using 2 generators at a time:\n   Completed Matrix  1:  lower =  3, upper =  7. Elapsed: 0.00s\nTermination predicted with 6 generators at matrix 1\nEnumerating using 3 generators at a time:\n   Completed Matrix  1:  lower =  4, upper =  7. Elapsed: 0.00s\nTermination predicted with 6 generators at matrix 1\nEnumerating using 4 generators at a time:\n   Completed Matrix  1:  lower =  5, upper =  7. Elapsed: 0.00s\nTermination predicted with 6 generators at matrix 1\nEnumerating using 5 generators at a time:\n   Completed Matrix  1:  lower =  6, upper =  7. Elapsed: 0.00s\nTermination predicted with 6 generators at matrix 1\nEnumerating using 6 generators at a time:\n   Completed Matrix  1:  lower =  7, upper =  7. Elapsed: 0.06s\nComputation complete \nFinal Results: lower = 7, upper = 7,\nTotal CPU time: 0.06, real time: 0.071\n7\n\nTotal time: 0.080 seconds, Total memory usage: 32.09MB\n
[[30,9,6]]	30	9	6	0	0.08552108399453573	1	1	Magma V2.28-26    Tue Mar  3 2026 21:16:29 on Marks-MacBook-Air-2 [Seed = \n703008615]\nType ? for help.  Type <Ctrl>-D to quit.\n[[30, 9]] quantum code over GF(2^2), stabilised by:\nQuantum GF(2)-Additive code over GF(4) of length 30 with 39 generators.\nLower Bound: 1, Upper Bound: 12\nConstructed 2 distinct generator matrices\nTotal Ranks:     20  20 \nRelative Ranks:  20  10 \n(4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2 )\n(4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2 )\nTime Taken: 0.00\nStarting search for low weight codewords... (reset timings)\nEnumerating using 1 generator at a time:\n     New codeword identified of weight 9, time 0.00\n     New codeword identified of weight 8, time 0.00\n     New codeword identified of weight 7, time 0.00\n     New codeword identified of weight 6, time 0.00\n     Discarding non-contributing rank 10 matrix\n     New Total Ranks:     20 \n     New Relative Ranks:  20 \n   Completed Matrix  1:  lower =  2, upper =  6. Elapsed: 0.00s\nTermination predicted with 5 generators at matrix 1\nEnumerating using 2 generators at a time:\n   Completed Matrix  1:  lower =  3, upper =  6. Elapsed: 0.00s\nTermination predicted with 5 generators at matrix 1\nEnumerating using 3 generators at a time:\n   Completed Matrix  1:  lower =  4, upper =  6. Elapsed: 0.00s\nTermination predicted with 5 generators at matrix 1\nEnumerating using 4 generators at a time:\n   Completed Matrix  1:  lower =  5, upper =  6. Elapsed: 0.00s\nTermination predicted with 5 generators at matrix 1\nEnumerating using 5 generators at a time:\n   Completed Matrix  1:  lower =  6, upper =  6. Elapsed: 0.02s\nComputation complete \nFinal Results: lower = 6, upper = 6,\nTotal CPU time: 0.02, real time: 0.022\n6\n\nTotal time: 0.030 seconds, Total memory usage: 32.09MB\n
[[31,9,6]]	31	9	6	0	0.09900158300297335	1	1	Magma V2.28-26    Tue Mar  3 2026 21:16:29 on Marks-MacBook-Air-2 [Seed = \n872224125]\nType ? for help.  Type <Ctrl>-D to quit.\n[[31, 9]] quantum code over GF(2^2), stabilised by:\nQuantum GF(2)-Additive code over GF(4) of length 31 with 40 generators.\nLower Bound: 1, Upper Bound: 12\nConstructed 2 distinct generator matrices\nTotal Ranks:     21  21 \nRelative Ranks:  21  10 \n(4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2 2 )\n(4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2 2 )\n     Discarding non-contributing rank 10 matrix\n     New Total Ranks:     21 \n     New Relative Ranks:  21 \nTime Taken: 0.00\nStarting search for low weight codewords... (reset timings)\nEnumerating using 1 generator at a time:\n     New codeword identified of weight 9, time 0.00\n     New codeword identified of weight 8, time 0.00\n     New codeword identified of weight 7, time 0.00\n     New codeword identified of weight 6, time 0.00\n     Impurity detected of weight 1, time 0.00\n   Completed Matrix  1:  lower =  2, upper =  6. Elapsed: 0.00s\nTermination predicted with 5 generators at matrix 1\nEnumerating using 2 generators at a time:\n   Completed Matrix  1:  lower =  3, upper =  6. Elapsed: 0.00s\nTermination predicted with 5 generators at matrix 1\nEnumerating using 3 generators at a time:\n   Completed Matrix  1:  lower =  4, upper =  6. Elapsed: 0.00s\nTermination predicted with 5 generators at matrix 1\nEnumerating using 4 generators at a time:\n   Completed Matrix  1:  lower =  5, upper =  6. Elapsed: 0.00s\nTermination predicted with 5 generators at matrix 1\nEnumerating using 5 generators at a time:\n   Completed Matrix  1:  lower =  6, upper =  6. Elapsed: 0.02s\nComputation complete \nFinal Results: lower = 6, upper = 6,\nTotal CPU time: 0.02, real time: 0.025\n6\n\nTotal time: 0.030 seconds, Total memory usage: 32.09MB\n
[[32,5,8]]	32	5	8	0	0.264886832999764	1	1	Magma V2.28-26    Tue Mar  3 2026 21:16:29 on Marks-MacBook-Air-2 [Seed = \n905646971]\nType ? for help.  Type <Ctrl>-D to quit.\n[[32, 5]] quantum code over GF(2^2), stabilised by:\nQuantum GF(2)-Additive code over GF(4) of length 32 with 37 generators.\nLower Bound: 1, Upper Bound: 15\nConstructed 2 distinct generator matrices\nTotal Ranks:     19  19 \nRelative Ranks:  19  13 \n(4 4 4 4 4 4 4 4 4 4 4 4 4 4 2 4 4 4 4 )\n(4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2 )\nTime Taken: 0.00\nStarting search for low weight codewords... (reset timings)\nEnumerating using 1 generator at a time:\n     New codeword identified of weight 9, time 0.00\n     Impurity detected of weight 1, time 0.00\n     New codeword identified of weight 8, time 0.00\n   Completed Matrix  1:  lower =  2, upper =  8. Elapsed: 0.00s\n   Completed Matrix  2:  lower =  2, upper =  8. Elapsed: 0.00s\nTermination predicted with 6 generators at matrix 2\nEnumerating using 2 generators at a time:\n   Completed Matrix  1:  lower =  3, upper =  8. Elapsed: 0.00s\n   Completed Matrix  2:  lower =  3, upper =  8. Elapsed: 0.00s\nTermination predicted with 6 generators at matrix 2\nEnumerating using 3 generators at a time:\n   Completed Matrix  1:  lower =  4, upper =  8. Elapsed: 0.00s\n   Completed Matrix  2:  lower =  4, upper =  8. Elapsed: 0.00s\nTermination predicted with 6 generators at matrix 2\nEnumerating using 4 generators at a time:\n   Completed Matrix  1:  lower =  5, upper =  8. Elapsed: 0.00s\n   Completed Matrix  2:  lower =  5, upper =  8. Elapsed: 0.00s\nTermination predicted with 6 generators at matrix 2\nEnumerating using 5 generators at a time:\n   Completed Matrix  1:  lower =  6, upper =  8. Elapsed: 0.02s\n   Completed Matrix  2:  lower =  6, upper =  8. Elapsed: 0.03s\nTermination predicted with 6 generators at matrix 2\nEnumerating using 6 generators at a time:\n   Completed Matrix  1:  lower =  7, upper =  8. Elapsed: 0.11s\n   Completed Matrix  2:  lower =  8, upper =  8. Elapsed: 0.20s\nComputation complete \nFinal Results: lower = 8, upper = 8,\nTotal CPU time: 0.20, real time: 0.202\n8\n\nTotal time: 0.210 seconds, Total memory usage: 32.09MB\n
[[33,7,8]]	33	7	8	0	1.2068087920197286	1	1	Magma V2.28-26    Tue Mar  3 2026 21:16:30 on Marks-MacBook-Air-2 [Seed = \n1072765298]\nType ? for help.  Type <Ctrl>-D to quit.\n[[33, 7]] quantum code over GF(2^2), stabilised by:\nQuantum GF(2)-Additive code over GF(4) of length 33 with 40 generators.\nLower Bound: 1, Upper Bound: 14\nConstructed 2 distinct generator matrices\nTotal Ranks:     20  20 \nRelative Ranks:  20  13 \n(4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 )\n(4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 )\nTime Taken: 0.00\nStarting search for low weight codewords... (reset timings)\nEnumerating using 1 generator at a time:\n     New codeword identified of weight 10, time 0.00\n     New codeword identified of weight 8, time 0.00\n     Discarding non-contributing rank 13 matrix\n     New Total Ranks:     20 \n     New Relative Ranks:  20 \n   Completed Matrix  1:  lower =  2, upper =  8. Elapsed: 0.00s\nTermination predicted with 7 generators at matrix 1\nEnumerating using 2 generators at a time:\n   Completed Matrix  1:  lower =  3, upper =  8. Elapsed: 0.00s\nTermination predicted with 7 generators at matrix 1\nEnumerating using 3 generators at a time:\n   Completed Matrix  1:  lower =  4, upper =  8. Elapsed: 0.00s\nTermination predicted with 7 generators at matrix 1\nEnumerating using 4 generators at a time:\n   Completed Matrix  1:  lower =  5, upper =  8. Elapsed: 0.00s\nTermination predicted with 7 generators at matrix 1\nEnumerating using 5 generators at a time:\n   Completed Matrix  1:  lower =  6, upper =  8. Elapsed: 0.02s\nTermination predicted with 7 generators at matrix 1\nEnumerating using 6 generators at a time:\n   Completed Matrix  1:  lower =  7, upper =  8. Elapsed: 0.18s\nTermination predicted with 7 generators at matrix 1\nEnumerating using 7 generators at a time:\n   Completed Matrix  1:  lower =  8, upper =  8. Elapsed: 1.12s\nComputation complete \nFinal Results: lower = 8, upper = 8,\nTotal CPU time: 1.12, real time: 1.139\n8\n\nTotal time: 1.139 seconds, Total memory usage: 32.09MB\n
[[34,17,5]]	34	17	5	0	0.08951387499109842	1	1	Magma V2.28-26    Tue Mar  3 2026 21:16:31 on Marks-MacBook-Air-2 [Seed = \n13510220]\nType ? for help.  Type <Ctrl>-D to quit.\n[[34, 17]] quantum code over GF(2^2), stabilised by:\nQuantum GF(2)-Additive code over GF(4) of length 34 with 51 generators.\nLower Bound: 1, Upper Bound: 10\nConstructed 2 distinct generator matrices\nTotal Ranks:     26  26 \nRelative Ranks:  26   8 \n(4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2 )\n(4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2 )\n     Discarding non-contributing rank 8 matrix\n     New Total Ranks:     26 \n     New Relative Ranks:  26 \nTime Taken: 0.00\nStarting search for low weight codewords... (reset timings)\nEnumerating using 1 generator at a time:\n     New codeword identified of weight 7, time 0.00\n     New codeword identified of weight 6, time 0.00\n   Completed Matrix  1:  lower =  2, upper =  6. Elapsed: 0.00s\nTermination predicted with 5 generators at matrix 1\nEnumerating using 2 generators at a time:\n     New codeword identified of weight 5, time 0.00\n   Completed Matrix  1:  lower =  3, upper =  5. Elapsed: 0.00s\nTermination predicted with 4 generators at matrix 1\nEnumerating using 3 generators at a time:\n   Completed Matrix  1:  lower =  4, upper =  5. Elapsed: 0.00s\nTermination predicted with 4 generators at matrix 1\nEnumerating using 4 generators at a time:\n   Completed Matrix  1:  lower =  5, upper =  5. Elapsed: 0.01s\nComputation complete \nFinal Results: lower = 5, upper = 5,\nTotal CPU time: 0.01, real time: 0.012\n5\n\nTotal time: 0.030 seconds, Total memory usage: 32.09MB\n
[[35,4,9]]	35	4	9	0	0.3711145829875022	1	1	Magma V2.28-26    Tue Mar  3 2026 21:16:31 on Marks-MacBook-Air-2 [Seed = \n180628550]\nType ? for help.  Type <Ctrl>-D to quit.\n[[35, 4]] quantum code over GF(2^2), stabilised by:\nQuantum GF(2)-Additive code over GF(4) of length 35 with 39 generators.\nLower Bound: 1, Upper Bound: 17\nConstructed 2 distinct generator matrices\nTotal Ranks:     20  20 \nRelative Ranks:  20  15 \n(4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2 )\n(4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2 )\nTime Taken: 0.00\nStarting search for low weight codewords... (reset timings)\nEnumerating using 1 generator at a time:\n     New codeword identified of weight 14, time 0.00\n     New codeword identified of weight 12, time 0.00\n     New codeword identified of weight 10, time 0.00\n   Completed Matrix  1:  lower =  2, upper = 10. Elapsed: 0.00s\n     New codeword identified of weight 9, time 0.00\n   Completed Matrix  2:  lower =  2, upper =  9. Elapsed: 0.00s\nTermination predicted with 6 generators at matrix 2\nEnumerating using 2 generators at a time:\n   Completed Matrix  1:  lower =  3, upper =  9. Elapsed: 0.00s\n   Completed Matrix  2:  lower =  3, upper =  9. Elapsed: 0.00s\nTermination predicted with 6 generators at matrix 2\nEnumerating using 3 generators at a time:\n   Completed Matrix  1:  lower =  4, upper =  9. Elapsed: 0.00s\n   Completed Matrix  2:  lower =  4, upper =  9. Elapsed: 0.00s\nTermination predicted with 6 generators at matrix 2\nEnumerating using 4 generators at a time:\n   Completed Matrix  1:  lower =  5, upper =  9. Elapsed: 0.00s\n   Completed Matrix  2:  lower =  5, upper =  9. Elapsed: 0.01s\nTermination predicted with 6 generators at matrix 2\nEnumerating using 5 generators at a time:\n   Completed Matrix  1:  lower =  6, upper =  9. Elapsed: 0.02s\n   Completed Matrix  2:  lower =  7, upper =  9. Elapsed: 0.04s\nTermination predicted with 6 generators at matrix 2\nEnumerating using 6 generators at a time:\n   Completed Matrix  1:  lower =  8, upper =  9. Elapsed: 0.17s\n   Completed Matrix  2:  lower =  9, upper =  9. Elapsed: 0.29s\nComputation complete \nFinal Results: lower = 9, upper = 9,\nTotal CPU time: 0.29, real time: 0.291\n9\n\nTotal time: 0.310 seconds, Total memory usage: 32.09MB\n
[[36,4,9]]	36	4	9	0	1.238300375000108	1	1	Magma V2.28-26    Tue Mar  3 2026 21:16:31 on Marks-MacBook-Air-2 [Seed = \n214051392]\nType ? for help.  Type <Ctrl>-D to quit.\n[[36, 4]] quantum code over GF(2^2), stabilised by:\nQuantum GF(2)-Additive code over GF(4) of length 36 with 40 generators.\nLower Bound: 1, Upper Bound: 17\nConstructed 2 distinct generator matrices\nTotal Ranks:     21  21 \nRelative Ranks:  21  15 \n(4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2 4 2 )\n(4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2 2 )\nTime Taken: 0.00\nStarting search for low weight codewords... (reset timings)\nEnumerating using 1 generator at a time:\n     New codeword identified of weight 14, time 0.00\n     New codeword identified of weight 9, time 0.00\n     Impurity detected of weight 1, time 0.00\n   Completed Matrix  1:  lower =  2, upper =  9. Elapsed: 0.00s\n   Completed Matrix  2:  lower =  2, upper =  9. Elapsed: 0.00s\nTermination predicted with 7 generators at matrix 1\nEnumerating using 2 generators at a time:\n   Completed Matrix  1:  lower =  3, upper =  9. Elapsed: 0.00s\n   Completed Matrix  2:  lower =  3, upper =  9. Elapsed: 0.00s\nTermination predicted with 7 generators at matrix 1\nEnumerating using 3 generators at a time:\n   Completed Matrix  1:  lower =  4, upper =  9. Elapsed: 0.00s\n   Completed Matrix  2:  lower =  4, upper =  9. Elapsed: 0.00s\nTermination predicted with 7 generators at matrix 1\nEnumerating using 4 generators at a time:\n   Completed Matrix  1:  lower =  5, upper =  9. Elapsed: 0.00s\n   Completed Matrix  2:  lower =  5, upper =  9. Elapsed: 0.00s\nTermination predicted with 7 generators at matrix 1\nEnumerating using 5 generators at a time:\n   Completed Matrix  1:  lower =  6, upper =  9. Elapsed: 0.02s\n   Completed Matrix  2:  lower =  6, upper =  9. Elapsed: 0.03s\nTermination predicted with 7 generators at matrix 1\nEnumerating using 6 generators at a time:\n   Completed Matrix  1:  lower =  7, upper =  9. Elapsed: 0.18s\n   Completed Matrix  2:  lower =  8, upper =  9. Elapsed: 0.32s\nTermination predicted at 1 s with 7 generators at matrix 1\nEnumerating using 7 generators at a time:\n   Completed Matrix  1:  lower =  9, upper =  9. Elapsed: 1.16s\nComputation complete \nFinal Results: lower = 9, upper = 9,\nTotal CPU time: 1.16, real time: 1.168\n9\n\nTotal time: 1.179 seconds, Total memory usage: 32.09MB\n
