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[[114,4,14]] d ≤
n
114
k
4
d
14
kd²/n
6.877
w
6

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Distance

d_X 14 · witness weight 14 (claimed upper_bound)
witness operator (support, 14 qubits)
[7, 11, 14, 15, 19, 29, 53, 55, 58, 66, 69, 80, 83, 95]
d_Z 14 · witness weight 14 (claimed upper_bound)
witness operator (support, 14 qubits)
[21, 28, 35, 36, 38, 39, 42, 45, 56, 60, 82, 89, 102, 104]
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-5 on the abelian quotient group Z2/L with twist basis a_1=[0, 3], a_2=[19, 1] (n=2|det[a_1,a_2]|=2*57). 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 57 · Z-checks 57
H_X (57 checks, sparse supports)
[0, 1, 53, 57, 59, 100] [1, 3, 55, 58, 61, 103] [2, 4, 45, 59, 62, 104] [3, 6, 56, 60, 64, 106] [4, 7, 48, 61, 65, 107] [5, 8, 49, 57, 62, 96] [2, 6, 9, 63, 67, 109] [7, 10, 51, 64, 68, 110] [8, 11, 52, 58, 65, 99] [4, 9, 12, 66, 70, 111] [5, 10, 13, 67, 71, 112] [11, 14, 54, 60, 68, 102] [7, 12, 15, 57, 69, 73] [8, 13, 16, 70, 74, 113] [0, 14, 17, 63, 71, 105] [10, 15, 18, 58, 72, 76] [11, 16, 19, 59, 73, 77] [1, 17, 20, 66, 74, 108] [13, 18, 21, 60, 75, 79] [14, 19, 22, 61, 76, 80] [3, 20, 23, 62, 69, 77] [16, 21, 24, 63, 78, 82] [17, 22, 25, 64, 79, 83] [6, 23, 26, 65, 72, 80] [19, 24, 27, 66, 81, 85] [20, 25, 28, 67, 82, 86] [9, 26, 29, 68, 75, 83] [22, 27, 30, 69, 84, 88] [23, 28, 31, 70, 85, 89] [12, 29, 32, 71, 78, 86] [25, 30, 33, 72, 87, 91] [26, 31, 34, 73, 88, 92] [15, 32, 35, 74, 81, 89] [28, 33, 36, 75, 90, 94] [29, 34, 37, 76, 91, 95] [18, 35, 38, 77, 84, 92] [31, 36, 39, 78, 93, 97] [32, 37, 40, 79, 94, 98] [21, 38, 41, 80, 87, 95] [34, 39, 42, 81, 96, 100] [35, 40, 43, 82, 97, 101] [24, 41, 44, 83, 90, 98] [37, 42, 45, 84, 99, 103] [38, 43, 46, 85, 100, 104] [27, 44, 47, 86, 93, 101] [40, 45, 48, 87, 102, 106] [41, 46, 49, 88, 103, 107] [30, 47, 50, 89, 96, 104] [43, 48, 51, 90, 105, 109] [44, 49, 52, 91, 106, 110] [33, 50, 53, 92, 99, 107] [5, 46, 51, 93, 108, 111] [47, 52, 54, 94, 109, 112] [36, 53, 55, 95, 102, 110] [0, 50, 54, 97, 111, 113] [39, 55, 56, 98, 105, 112] [2, 42, 56, 101, 108, 113]
H_Z (57 checks, sparse supports)
[0, 5, 12, 57, 71, 111] [1, 8, 15, 57, 58, 74] [0, 2, 16, 59, 63, 113] [3, 11, 18, 58, 60, 77] [1, 4, 19, 59, 61, 66] [2, 5, 20, 62, 67, 108] [6, 14, 21, 60, 63, 80] [3, 7, 22, 61, 64, 69] [4, 8, 23, 62, 65, 70] [9, 17, 24, 63, 66, 83] [6, 10, 25, 64, 67, 72] [7, 11, 26, 65, 68, 73] [12, 20, 27, 66, 69, 86] [9, 13, 28, 67, 70, 75] [10, 14, 29, 68, 71, 76] [15, 23, 30, 69, 72, 89] [12, 16, 31, 70, 73, 78] [13, 17, 32, 71, 74, 79] [18, 26, 33, 72, 75, 92] [15, 19, 34, 73, 76, 81] [16, 20, 35, 74, 77, 82] [21, 29, 36, 75, 78, 95] [18, 22, 37, 76, 79, 84] [19, 23, 38, 77, 80, 85] [24, 32, 39, 78, 81, 98] [21, 25, 40, 79, 82, 87] [22, 26, 41, 80, 83, 88] [27, 35, 42, 81, 84, 101] [24, 28, 43, 82, 85, 90] [25, 29, 44, 83, 86, 91] [30, 38, 45, 84, 87, 104] [27, 31, 46, 85, 88, 93] [28, 32, 47, 86, 89, 94] [33, 41, 48, 87, 90, 107] [30, 34, 49, 88, 91, 96] [31, 35, 50, 89, 92, 97] [36, 44, 51, 90, 93, 110] [33, 37, 52, 91, 94, 99] [34, 38, 53, 92, 95, 100] [5, 39, 47, 93, 96, 112] [36, 40, 54, 94, 97, 102] [37, 41, 55, 95, 98, 103] [8, 42, 50, 96, 99, 113] [0, 39, 43, 97, 100, 105] [40, 44, 56, 98, 101, 106] [11, 45, 53, 59, 99, 102] [1, 42, 46, 100, 103, 108] [2, 43, 47, 101, 104, 109] [14, 48, 55, 61, 102, 105] [3, 45, 49, 62, 103, 106] [4, 46, 50, 104, 107, 111] [17, 51, 56, 64, 105, 108] [6, 48, 52, 65, 106, 109] [7, 49, 53, 57, 107, 110] [9, 51, 54, 68, 109, 111] [10, 52, 55, 58, 110, 112] [13, 54, 56, 60, 112, 113]
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