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[[204,4,20]] d ≤
n
204
k
4
d
20
kd²/n
7.843
w
6

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Distance

d_X 20 · witness weight 20 (claimed upper_bound)
witness operator (support, 20 qubits)
[26, 37, 44, 47, 49, 57, 72, 79, 82, 95, 119, 128, 129, 131, 143, 151, 160, 178, 193, 198]
d_Z 20 · witness weight 20 (claimed upper_bound)
witness operator (support, 20 qubits)
[12, 21, 29, 47, 53, 54, 62, 71, 76, 79, 98, 102, 117, 159, 166, 169, 196, 197, 201, 203]
certificate none yet · distance stands as a self-certified upper bound (d ≤)

Construction & provenance

authors Zijian Liang and Ke Liu and Hao Song and Yu-An Chen
provenance literature baseline
construction Twisted-torus bivariate-bicycle code from Generalized toric codes on twisted tori for quantum error correction (PRX Quantum 6, 020357, 2025). Stabilizers f(x,y)=1+x+x-3y, g(x,y)=1+y+x-1y-2 on the abelian quotient group Z2/L with twist basis a_1=[0, 51], a_2=[2, 14] (n=2|det[a_1,a_2]|=2*102). Reconstructed from the published polynomials and twist; CSS form H_X=[f|g], H_Z=[gbar|fbar].
model classical construction (no AI model)
reference arXiv:2503.03827
date 2025
notes Reconstructed baseline from Liang, Liu, Song, Chen, Generalized toric codes on twisted tori for quantum error correction (PRX Quantum 6, 020357, 2025), arXiv:2503.03827. The [[n,k,d]] parameter set and stabilizer polynomials are published in that paper; this entry reproduces them. Distance is an upper bound per the paper (probabilistic for d>20); the witness is the surrogate logical of that weight. Seeded to fill a board coverage gap at this block size, not a discovery.
family bivariate bicycle (a tag, not a ranking)
locality unrestricted (computed from the layout)
weight class weight ≤ 6 (computed)

How this code was found

no research note was staged with this submission — notes are requested for new submissions (notes/README.md)

Parity checks

X-checks 102 · Z-checks 102
H_X (102 checks, sparse supports)
[0, 1, 69, 102, 104, 159] [1, 3, 78, 103, 106, 168] [2, 4, 79, 104, 107, 169] [3, 6, 86, 105, 109, 177] [4, 7, 87, 106, 110, 178] [5, 8, 88, 107, 111, 179] [2, 6, 10, 108, 113, 186] [7, 11, 93, 109, 114, 187] [8, 12, 94, 102, 110, 115] [9, 13, 63, 111, 116, 188] [4, 10, 15, 112, 118, 193] [5, 11, 16, 113, 119, 194] [12, 17, 98, 103, 114, 120] [13, 18, 72, 104, 115, 121] [14, 19, 73, 116, 122, 195] [7, 15, 21, 117, 124, 198] [8, 16, 22, 118, 125, 199] [9, 17, 23, 105, 119, 126] [18, 24, 81, 106, 120, 127] [19, 25, 82, 107, 121, 128] [20, 26, 83, 122, 129, 200] [11, 21, 28, 123, 131, 201] [12, 22, 29, 124, 132, 202] [13, 23, 30, 108, 125, 133] [14, 24, 31, 109, 126, 134] [25, 32, 89, 110, 127, 135] [26, 33, 90, 111, 128, 136] [27, 34, 91, 129, 137, 183] [16, 28, 36, 130, 137, 139] [17, 29, 37, 131, 140, 203] [18, 30, 38, 112, 132, 141] [19, 31, 39, 113, 133, 142] [20, 32, 40, 114, 134, 143] [33, 41, 95, 115, 135, 144] [34, 42, 96, 116, 136, 145] [35, 43, 97, 137, 146, 191] [22, 36, 45, 138, 145, 148] [23, 37, 46, 139, 146, 149] [24, 38, 47, 117, 140, 150] [25, 39, 48, 118, 141, 151] [26, 40, 49, 119, 142, 152] [27, 41, 50, 120, 143, 153] [42, 51, 99, 121, 144, 154] [43, 52, 100, 122, 145, 155] [6, 44, 53, 123, 146, 197] [29, 45, 54, 147, 154, 157] [30, 46, 55, 148, 155, 158] [31, 47, 56, 123, 149, 159] [32, 48, 57, 124, 150, 160] [33, 49, 58, 125, 151, 161] [34, 50, 59, 126, 152, 162] [35, 51, 60, 127, 153, 163] [52, 61, 101, 128, 154, 164] [10, 53, 62, 129, 130, 155] [37, 54, 63, 156, 163, 166] [38, 55, 64, 157, 164, 167] [39, 56, 65, 130, 158, 168] [40, 57, 66, 131, 159, 169] [41, 58, 67, 132, 160, 170] [42, 59, 68, 133, 161, 171] [43, 60, 69, 134, 162, 172] [44, 61, 70, 135, 163, 173] [15, 62, 71, 136, 138, 164] [46, 63, 72, 165, 172, 175] [47, 64, 73, 166, 173, 176] [48, 65, 74, 138, 167, 177] [49, 66, 75, 139, 168, 178] [50, 67, 76, 140, 169, 179] [51, 68, 77, 141, 170, 180] [52, 69, 78, 142, 171, 181] [53, 70, 79, 143, 172, 182] [21, 71, 80, 144, 147, 173] [55, 72, 81, 174, 181, 184] [56, 73, 82, 175, 182, 185] [57, 74, 83, 147, 176, 186] [58, 75, 84, 148, 177, 187] [59, 76, 85, 102, 149, 178] [0, 60, 77, 150, 179, 188] [61, 78, 86, 151, 180, 189] [62, 79, 87, 152, 181, 190] [28, 80, 88, 153, 156, 182] [14, 64, 81, 183, 189, 191] [65, 82, 89, 184, 190, 192] [66, 83, 90, 156, 185, 193] [67, 84, 91, 157, 186, 194] [68, 85, 92, 103, 158, 187] [2, 70, 86, 160, 188, 195] [71, 87, 93, 161, 189, 196] [36, 88, 94, 162, 165, 190] [20, 74, 89, 191, 196, 197] [75, 90, 95, 165, 192, 198] [76, 91, 96, 166, 193, 199] [77, 92, 97, 105, 167, 194] [5, 80, 93, 170, 195, 200] [45, 94, 98, 171, 174, 196] [27, 84, 95, 174, 197, 201] [85, 96, 99, 175, 198, 202] [0, 97, 100, 108, 176, 199] [9, 54, 98, 180, 183, 200] [35, 92, 99, 184, 201, 203] [1, 100, 101, 112, 185, 202] [3, 44, 101, 117, 192, 203]
H_Z (102 checks, sparse supports)
[0, 8, 76, 102, 179, 199] [1, 12, 85, 102, 103, 202] [0, 2, 13, 104, 108, 188] [3, 17, 92, 103, 105, 203] [1, 4, 18, 104, 106, 112] [2, 5, 19, 107, 113, 195] [6, 23, 97, 105, 108, 146] [3, 7, 24, 106, 109, 117] [4, 8, 25, 107, 110, 118] [5, 9, 26, 111, 119, 200] [10, 30, 100, 108, 112, 155] [6, 11, 31, 109, 113, 123] [7, 12, 32, 110, 114, 124] [8, 13, 33, 111, 115, 125] [9, 14, 34, 116, 126, 183] [15, 38, 101, 112, 117, 164] [10, 16, 39, 113, 118, 130] [11, 17, 40, 114, 119, 131] [12, 18, 41, 115, 120, 132] [13, 19, 42, 116, 121, 133] [14, 20, 43, 122, 134, 191] [21, 44, 47, 117, 123, 173] [15, 22, 48, 118, 124, 138] [16, 23, 49, 119, 125, 139] [17, 24, 50, 120, 126, 140] [18, 25, 51, 121, 127, 141] [19, 26, 52, 122, 128, 142] [20, 27, 53, 129, 143, 197] [28, 53, 56, 123, 130, 182] [21, 29, 57, 124, 131, 147] [22, 30, 58, 125, 132, 148] [23, 31, 59, 126, 133, 149] [24, 32, 60, 127, 134, 150] [25, 33, 61, 128, 135, 151] [26, 34, 62, 129, 136, 152] [27, 28, 35, 137, 153, 201] [36, 62, 65, 130, 138, 190] [28, 37, 66, 131, 139, 156] [29, 38, 67, 132, 140, 157] [30, 39, 68, 133, 141, 158] [31, 40, 69, 134, 142, 159] [32, 41, 70, 135, 143, 160] [33, 42, 71, 136, 144, 161] [34, 36, 43, 137, 145, 162] [35, 37, 44, 146, 163, 203] [45, 71, 74, 138, 147, 196] [36, 46, 75, 139, 148, 165] [37, 47, 76, 140, 149, 166] [38, 48, 77, 141, 150, 167] [39, 49, 78, 142, 151, 168] [40, 50, 79, 143, 152, 169] [41, 51, 80, 144, 153, 170] [42, 45, 52, 145, 154, 171] [43, 46, 53, 146, 155, 172] [54, 80, 83, 147, 156, 200] [45, 55, 84, 148, 157, 174] [46, 56, 85, 149, 158, 175] [0, 47, 57, 150, 159, 176] [48, 58, 86, 151, 160, 177] [49, 59, 87, 152, 161, 178] [50, 60, 88, 153, 162, 179] [51, 54, 61, 154, 163, 180] [52, 55, 62, 155, 164, 181] [63, 88, 90, 111, 156, 165] [54, 64, 91, 157, 166, 183] [55, 65, 92, 158, 167, 184] [1, 56, 66, 159, 168, 185] [2, 57, 67, 160, 169, 186] [58, 68, 93, 161, 170, 187] [59, 69, 94, 102, 162, 171] [60, 63, 70, 163, 172, 188] [61, 64, 71, 164, 173, 189] [72, 94, 95, 115, 165, 174] [63, 73, 96, 116, 166, 175] [64, 74, 97, 167, 176, 191] [3, 65, 75, 168, 177, 192] [4, 66, 76, 169, 178, 193] [5, 67, 77, 170, 179, 194] [68, 78, 98, 103, 171, 180] [69, 72, 79, 104, 172, 181] [70, 73, 80, 173, 182, 195] [27, 81, 98, 120, 174, 183] [72, 82, 99, 121, 175, 184] [73, 83, 100, 122, 176, 185] [6, 74, 84, 177, 186, 197] [7, 75, 85, 178, 187, 198] [9, 77, 86, 105, 180, 188] [78, 81, 87, 106, 181, 189] [79, 82, 88, 107, 182, 190] [35, 81, 89, 127, 184, 191] [82, 90, 101, 128, 185, 192] [10, 83, 91, 129, 186, 193] [11, 84, 92, 187, 194, 201] [14, 86, 93, 109, 189, 195] [87, 89, 94, 110, 190, 196] [44, 89, 95, 135, 192, 197] [15, 90, 96, 136, 193, 198] [16, 91, 97, 137, 194, 199] [20, 93, 98, 114, 196, 200] [21, 95, 99, 144, 198, 201] [22, 96, 100, 145, 199, 202] [29, 99, 101, 154, 202, 203]
raw submission JSON