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[[120,8,12]] d =
n
120
k
8
d
12
kd²/n
9.6
w
6

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Distance

d_X 12 · witness weight 12 (claimed upper_bound)
witness operator (support, 12 qubits)
[18, 29, 48, 59, 70, 73, 76, 89, 100, 103, 106, 119]
d_Z 12 · witness weight 12 (claimed upper_bound)
witness operator (support, 12 qubits)
[6, 27, 33, 37, 41, 62, 72, 74, 76, 91, 98, 110]
certificate exact, d = 12 · CryptoMiniSat 5.14 SAT
X: no logical < 12 exists (CryptoMiniSat, XOR + sequential-counter cardinality); Z: no logical < 12 exists (CryptoMiniSat, XOR + sequential-counter cardinality)

Construction & provenance

authors @FarLab
provenance submitted through the challenge
novelty known parameter set; see provenance notes
construction Bivariate bicycle on Z_12 x Z_5, A=[[9, 2], [2, 4], [11, 0]], B=[[7, 4], [4, 2], [0, 3]]. Generated by automated random search over the bivariate-bicycle family (autoresearch pilot). The surrogate distance is an UPPER BOUND that converged and stayed stable through 16k random-restart trials. confidence=upper_bound: distance is NOT exactly certified. Known-parameter status is recorded in provenance.notes.
model Claude Claude Opus 4.8 (claimed, not verified)
builds on arXiv:2308.07915
date 2026-06-26
notes The [[120,8,12]] parameter set is already published: a weight-8 self-dual bivariate-bicycle code (arXiv:2510.05211), and twisted-torus / generalized-toric codes (arXiv:2503.03827, arXiv:2606.17268). This entry is weight-6, so it improves on the weight-8 version, but the parameters are not novel; a code-equivalence audit is pending. Do not present it as a novel-parameter 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 60 · Z-checks 60
H_X (60 checks, sparse supports)
[14, 47, 55, 63, 82, 99] [10, 48, 56, 64, 83, 95] [11, 49, 57, 60, 84, 96] [12, 45, 58, 61, 80, 97] [13, 46, 59, 62, 81, 98] [0, 19, 52, 68, 87, 104] [1, 15, 53, 69, 88, 100] [2, 16, 54, 65, 89, 101] [3, 17, 50, 66, 85, 102] [4, 18, 51, 67, 86, 103] [5, 24, 57, 73, 92, 109] [6, 20, 58, 74, 93, 105] [7, 21, 59, 70, 94, 106] [8, 22, 55, 71, 90, 107] [9, 23, 56, 72, 91, 108] [2, 10, 29, 78, 97, 114] [3, 11, 25, 79, 98, 110] [4, 12, 26, 75, 99, 111] [0, 13, 27, 76, 95, 112] [1, 14, 28, 77, 96, 113] [7, 15, 34, 83, 102, 119] [8, 16, 30, 84, 103, 115] [9, 17, 31, 80, 104, 116] [5, 18, 32, 81, 100, 117] [6, 19, 33, 82, 101, 118] [12, 20, 39, 64, 88, 107] [13, 21, 35, 60, 89, 108] [14, 22, 36, 61, 85, 109] [10, 23, 37, 62, 86, 105] [11, 24, 38, 63, 87, 106] [17, 25, 44, 69, 93, 112] [18, 26, 40, 65, 94, 113] [19, 27, 41, 66, 90, 114] [15, 28, 42, 67, 91, 110] [16, 29, 43, 68, 92, 111] [22, 30, 49, 74, 98, 117] [23, 31, 45, 70, 99, 118] [24, 32, 46, 71, 95, 119] [20, 33, 47, 72, 96, 115] [21, 34, 48, 73, 97, 116] [27, 35, 54, 62, 79, 103] [28, 36, 50, 63, 75, 104] [29, 37, 51, 64, 76, 100] [25, 38, 52, 60, 77, 101] [26, 39, 53, 61, 78, 102] [32, 40, 59, 67, 84, 108] [33, 41, 55, 68, 80, 109] [34, 42, 56, 69, 81, 105] [30, 43, 57, 65, 82, 106] [31, 44, 58, 66, 83, 107] [4, 37, 45, 72, 89, 113] [0, 38, 46, 73, 85, 114] [1, 39, 47, 74, 86, 110] [2, 35, 48, 70, 87, 111] [3, 36, 49, 71, 88, 112] [9, 42, 50, 77, 94, 118] [5, 43, 51, 78, 90, 119] [6, 44, 52, 79, 91, 115] [7, 40, 53, 75, 92, 116] [8, 41, 54, 76, 93, 117]
H_Z (60 checks, sparse supports)
[2, 26, 43, 65, 78, 111] [3, 27, 44, 66, 79, 112] [4, 28, 40, 67, 75, 113] [0, 29, 41, 68, 76, 114] [1, 25, 42, 69, 77, 110] [7, 31, 48, 70, 83, 116] [8, 32, 49, 71, 84, 117] [9, 33, 45, 72, 80, 118] [5, 34, 46, 73, 81, 119] [6, 30, 47, 74, 82, 115] [12, 36, 53, 61, 75, 88] [13, 37, 54, 62, 76, 89] [14, 38, 50, 63, 77, 85] [10, 39, 51, 64, 78, 86] [11, 35, 52, 60, 79, 87] [17, 41, 58, 66, 80, 93] [18, 42, 59, 67, 81, 94] [19, 43, 55, 68, 82, 90] [15, 44, 56, 69, 83, 91] [16, 40, 57, 65, 84, 92] [3, 22, 46, 71, 85, 98] [4, 23, 47, 72, 86, 99] [0, 24, 48, 73, 87, 95] [1, 20, 49, 74, 88, 96] [2, 21, 45, 70, 89, 97] [8, 27, 51, 76, 90, 103] [9, 28, 52, 77, 91, 104] [5, 29, 53, 78, 92, 100] [6, 25, 54, 79, 93, 101] [7, 26, 50, 75, 94, 102] [13, 32, 56, 81, 95, 108] [14, 33, 57, 82, 96, 109] [10, 34, 58, 83, 97, 105] [11, 30, 59, 84, 98, 106] [12, 31, 55, 80, 99, 107] [1, 18, 37, 86, 100, 113] [2, 19, 38, 87, 101, 114] [3, 15, 39, 88, 102, 110] [4, 16, 35, 89, 103, 111] [0, 17, 36, 85, 104, 112] [6, 23, 42, 91, 105, 118] [7, 24, 43, 92, 106, 119] [8, 20, 44, 93, 107, 115] [9, 21, 40, 94, 108, 116] [5, 22, 41, 90, 109, 117] [11, 28, 47, 63, 96, 110] [12, 29, 48, 64, 97, 111] [13, 25, 49, 60, 98, 112] [14, 26, 45, 61, 99, 113] [10, 27, 46, 62, 95, 114] [16, 33, 52, 68, 101, 115] [17, 34, 53, 69, 102, 116] [18, 30, 54, 65, 103, 117] [19, 31, 50, 66, 104, 118] [15, 32, 51, 67, 100, 119] [21, 38, 57, 60, 73, 106] [22, 39, 58, 61, 74, 107] [23, 35, 59, 62, 70, 108] [24, 36, 55, 63, 71, 109] [20, 37, 56, 64, 72, 105]
raw submission JSON