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[[174,4,18]] d ≤
n
174
k
4
d
18
kd²/n
7.448
w
6

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Distance

d_X 18 · witness weight 18 (claimed upper_bound)
witness operator (support, 18 qubits)
[21, 22, 39, 43, 45, 52, 53, 65, 67, 75, 97, 100, 109, 123, 133, 140, 153, 159]
d_Z 18 · witness weight 18 (claimed upper_bound)
witness operator (support, 18 qubits)
[15, 22, 25, 28, 48, 64, 83, 101, 106, 111, 115, 133, 147, 148, 165, 169, 170, 172]
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-8y, g(x,y)=1+y+x6y2 on the abelian quotient group Z2/L with twist basis a_1=[0, 3], a_2=[29, 1] (n=2|det[a_1,a_2]|=2*87). 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 87 · Z-checks 87
H_X (87 checks, sparse supports)
[0, 1, 68, 87, 89, 110] [1, 3, 71, 88, 91, 113] [2, 4, 60, 89, 92, 102] [3, 6, 74, 90, 94, 116] [4, 7, 63, 91, 95, 105] [5, 8, 64, 87, 92, 106] [6, 9, 77, 93, 97, 119] [7, 10, 66, 94, 98, 108] [8, 11, 67, 88, 95, 109] [9, 12, 80, 96, 100, 122] [10, 13, 69, 97, 101, 111] [11, 14, 70, 90, 98, 112] [12, 15, 83, 99, 103, 125] [13, 16, 72, 100, 104, 114] [14, 17, 73, 93, 101, 115] [15, 18, 85, 102, 106, 128] [16, 19, 75, 103, 107, 117] [17, 20, 76, 96, 104, 118] [18, 21, 86, 105, 109, 131] [19, 22, 78, 106, 110, 120] [20, 23, 79, 99, 107, 121] [2, 21, 24, 108, 112, 134] [22, 25, 81, 109, 113, 123] [23, 26, 82, 102, 110, 124] [4, 24, 27, 111, 115, 137] [5, 25, 28, 112, 116, 126] [26, 29, 84, 105, 113, 127] [7, 27, 30, 114, 118, 140] [8, 28, 31, 115, 119, 129] [0, 29, 32, 108, 116, 130] [10, 30, 33, 117, 121, 143] [11, 31, 34, 118, 122, 132] [1, 32, 35, 111, 119, 133] [13, 33, 36, 120, 124, 146] [14, 34, 37, 121, 125, 135] [3, 35, 38, 114, 122, 136] [16, 36, 39, 123, 127, 149] [17, 37, 40, 124, 128, 138] [6, 38, 41, 117, 125, 139] [19, 39, 42, 126, 130, 152] [20, 40, 43, 127, 131, 141] [9, 41, 44, 120, 128, 142] [22, 42, 45, 129, 133, 155] [23, 43, 46, 130, 134, 144] [12, 44, 47, 123, 131, 145] [25, 45, 48, 132, 136, 158] [26, 46, 49, 133, 137, 147] [15, 47, 50, 126, 134, 148] [28, 48, 51, 135, 139, 161] [29, 49, 52, 136, 140, 150] [18, 50, 53, 129, 137, 151] [31, 51, 54, 138, 142, 164] [32, 52, 55, 139, 143, 153] [21, 53, 56, 132, 140, 154] [34, 54, 57, 141, 145, 167] [35, 55, 58, 142, 146, 156] [24, 56, 59, 135, 143, 157] [37, 57, 60, 144, 148, 170] [38, 58, 61, 145, 149, 159] [27, 59, 62, 138, 146, 160] [40, 60, 63, 147, 151, 172] [41, 61, 64, 148, 152, 162] [30, 62, 65, 141, 149, 163] [43, 63, 66, 150, 154, 173] [44, 64, 67, 151, 155, 165] [33, 65, 68, 144, 152, 166] [46, 66, 69, 89, 153, 157] [47, 67, 70, 154, 158, 168] [36, 68, 71, 147, 155, 169] [49, 69, 72, 91, 156, 160] [50, 70, 73, 92, 157, 161] [39, 71, 74, 150, 158, 171] [52, 72, 75, 94, 159, 163] [53, 73, 76, 95, 160, 164] [42, 74, 77, 87, 153, 161] [55, 75, 78, 97, 162, 166] [56, 76, 79, 98, 163, 167] [45, 77, 80, 88, 156, 164] [58, 78, 81, 100, 165, 169] [59, 79, 82, 101, 166, 170] [48, 80, 83, 90, 159, 167] [5, 61, 81, 103, 168, 171] [62, 82, 84, 104, 169, 172] [51, 83, 85, 93, 162, 170] [0, 65, 84, 107, 171, 173] [54, 85, 86, 96, 165, 172] [2, 57, 86, 99, 168, 173]
H_Z (87 checks, sparse supports)
[0, 5, 74, 87, 116, 171] [1, 8, 77, 87, 88, 119] [0, 2, 66, 89, 108, 173] [3, 11, 80, 88, 90, 122] [1, 4, 69, 89, 91, 111] [2, 5, 70, 92, 112, 168] [6, 14, 83, 90, 93, 125] [3, 7, 72, 91, 94, 114] [4, 8, 73, 92, 95, 115] [9, 17, 85, 93, 96, 128] [6, 10, 75, 94, 97, 117] [7, 11, 76, 95, 98, 118] [12, 20, 86, 96, 99, 131] [9, 13, 78, 97, 100, 120] [10, 14, 79, 98, 101, 121] [2, 15, 23, 99, 102, 134] [12, 16, 81, 100, 103, 123] [13, 17, 82, 101, 104, 124] [4, 18, 26, 102, 105, 137] [5, 15, 19, 103, 106, 126] [16, 20, 84, 104, 107, 127] [7, 21, 29, 105, 108, 140] [8, 18, 22, 106, 109, 129] [0, 19, 23, 107, 110, 130] [10, 24, 32, 108, 111, 143] [11, 21, 25, 109, 112, 132] [1, 22, 26, 110, 113, 133] [13, 27, 35, 111, 114, 146] [14, 24, 28, 112, 115, 135] [3, 25, 29, 113, 116, 136] [16, 30, 38, 114, 117, 149] [17, 27, 31, 115, 118, 138] [6, 28, 32, 116, 119, 139] [19, 33, 41, 117, 120, 152] [20, 30, 34, 118, 121, 141] [9, 31, 35, 119, 122, 142] [22, 36, 44, 120, 123, 155] [23, 33, 37, 121, 124, 144] [12, 34, 38, 122, 125, 145] [25, 39, 47, 123, 126, 158] [26, 36, 40, 124, 127, 147] [15, 37, 41, 125, 128, 148] [28, 42, 50, 126, 129, 161] [29, 39, 43, 127, 130, 150] [18, 40, 44, 128, 131, 151] [31, 45, 53, 129, 132, 164] [32, 42, 46, 130, 133, 153] [21, 43, 47, 131, 134, 154] [34, 48, 56, 132, 135, 167] [35, 45, 49, 133, 136, 156] [24, 46, 50, 134, 137, 157] [37, 51, 59, 135, 138, 170] [38, 48, 52, 136, 139, 159] [27, 49, 53, 137, 140, 160] [40, 54, 62, 138, 141, 172] [41, 51, 55, 139, 142, 162] [30, 52, 56, 140, 143, 163] [43, 57, 65, 141, 144, 173] [44, 54, 58, 142, 145, 165] [33, 55, 59, 143, 146, 166] [46, 60, 68, 89, 144, 147] [47, 57, 61, 145, 148, 168] [36, 58, 62, 146, 149, 169] [49, 63, 71, 91, 147, 150] [50, 60, 64, 92, 148, 151] [39, 61, 65, 149, 152, 171] [52, 66, 74, 94, 150, 153] [53, 63, 67, 95, 151, 154] [42, 64, 68, 87, 152, 155] [55, 69, 77, 97, 153, 156] [56, 66, 70, 98, 154, 157] [45, 67, 71, 88, 155, 158] [58, 72, 80, 100, 156, 159] [59, 69, 73, 101, 157, 160] [48, 70, 74, 90, 158, 161] [61, 75, 83, 103, 159, 162] [62, 72, 76, 104, 160, 163] [51, 73, 77, 93, 161, 164] [64, 78, 85, 106, 162, 165] [65, 75, 79, 107, 163, 166] [54, 76, 80, 96, 164, 167] [67, 81, 86, 109, 165, 168] [68, 78, 82, 110, 166, 169] [57, 79, 83, 99, 167, 170] [71, 81, 84, 113, 169, 171] [60, 82, 85, 102, 170, 172] [63, 84, 86, 105, 172, 173]
raw submission JSON