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[[140,10,10]] d =
n
140
k
10
d
10
kd²/n
7.143
w
8

Share this result

Distance

d_X 10 · witness weight 10 (claimed upper_bound)
witness operator (support, 10 qubits)
[77, 80, 91, 94, 105, 108, 119, 122, 133, 136]
d_Z 10 · witness weight 10 (claimed upper_bound)
witness operator (support, 10 qubits)
[4, 5, 18, 19, 32, 33, 46, 47, 60, 61]
certificate exact, d = 10 · CryptoMiniSat 5.14 SAT
X: no logical < 10 exists (CryptoMiniSat, XOR + sequential-counter cardinality); Z: no logical < 10 exists (CryptoMiniSat, XOR + sequential-counter cardinality)

Construction & provenance

authors @mathysrennela
provenance submitted through the challenge
novelty novelty not audited
construction Two-block group-algebra code on metacyclic group Z_35 |x Z_2 (r=6), supports a=[7,33,54,66], b=[22,26,38,60].
model Tencent Hy3 (claimed, not verified)
builds on arXiv:2306.16400
date 2026-07-18
family generalized bicycle (a tag, not a ranking)
locality unrestricted (computed from the layout)
weight class weight ≤ 8 (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 70 · Z-checks 70
H_X (70 checks, sparse supports)
[4, 16, 19, 35, 80, 102, 114, 118] [5, 17, 18, 34, 79, 123, 125, 131] [6, 18, 31, 47, 82, 104, 116, 120] [7, 19, 30, 46, 81, 125, 127, 133] [8, 20, 43, 59, 84, 106, 118, 122] [9, 21, 42, 58, 83, 127, 129, 135] [1, 10, 22, 55, 86, 108, 120, 124] [0, 11, 23, 54, 85, 129, 131, 137] [12, 13, 24, 67, 88, 110, 122, 126] [12, 13, 25, 66, 87, 131, 133, 139] [9, 14, 25, 26, 90, 112, 124, 128] [8, 15, 24, 27, 71, 89, 133, 135] [16, 21, 28, 37, 92, 114, 126, 130] [17, 20, 29, 36, 73, 91, 135, 137] [18, 30, 33, 49, 94, 116, 128, 132] [19, 31, 32, 48, 75, 93, 137, 139] [20, 32, 45, 61, 96, 118, 130, 134] [21, 33, 44, 60, 71, 77, 95, 139] [3, 22, 34, 57, 98, 120, 132, 136] [2, 23, 35, 56, 71, 73, 79, 97] [15, 24, 36, 69, 100, 122, 134, 138] [14, 25, 37, 68, 73, 75, 81, 99] [11, 26, 27, 38, 70, 102, 124, 136] [10, 26, 27, 39, 75, 77, 83, 101] [23, 28, 39, 40, 72, 104, 126, 138] [22, 29, 38, 41, 77, 79, 85, 103] [30, 35, 42, 51, 70, 74, 106, 128] [31, 34, 43, 50, 79, 81, 87, 105] [32, 44, 47, 63, 72, 76, 108, 130] [33, 45, 46, 62, 81, 83, 89, 107] [5, 34, 46, 59, 74, 78, 110, 132] [4, 35, 47, 58, 83, 85, 91, 109] [1, 17, 36, 48, 76, 80, 112, 134] [0, 16, 37, 49, 85, 87, 93, 111] [13, 29, 38, 50, 78, 82, 114, 136] [12, 28, 39, 51, 87, 89, 95, 113] [25, 40, 41, 52, 80, 84, 116, 138] [24, 40, 41, 53, 89, 91, 97, 115] [37, 42, 53, 54, 70, 82, 86, 118] [36, 43, 52, 55, 91, 93, 99, 117] [44, 49, 56, 65, 72, 84, 88, 120] [45, 48, 57, 64, 93, 95, 101, 119] [7, 46, 58, 61, 74, 86, 90, 122] [6, 47, 59, 60, 95, 97, 103, 121] [3, 19, 48, 60, 76, 88, 92, 124] [2, 18, 49, 61, 97, 99, 105, 123] [15, 31, 50, 62, 78, 90, 94, 126] [14, 30, 51, 63, 99, 101, 107, 125] [27, 43, 52, 64, 80, 92, 96, 128] [26, 42, 53, 65, 101, 103, 109, 127] [39, 54, 55, 66, 82, 94, 98, 130] [38, 54, 55, 67, 103, 105, 111, 129] [51, 56, 67, 68, 84, 96, 100, 132] [50, 57, 66, 69, 105, 107, 113, 131] [0, 9, 58, 63, 86, 98, 102, 134] [1, 8, 59, 62, 107, 109, 115, 133] [2, 5, 21, 60, 88, 100, 104, 136] [3, 4, 20, 61, 109, 111, 117, 135] [4, 17, 33, 62, 90, 102, 106, 138] [5, 16, 32, 63, 111, 113, 119, 137] [6, 29, 45, 64, 70, 92, 104, 108] [7, 28, 44, 65, 113, 115, 121, 139] [8, 41, 57, 66, 72, 94, 106, 110] [9, 40, 56, 67, 71, 115, 117, 123] [10, 53, 68, 69, 74, 96, 108, 112] [11, 52, 68, 69, 73, 117, 119, 125] [0, 11, 12, 65, 76, 98, 110, 114] [1, 10, 13, 64, 75, 119, 121, 127] [2, 7, 14, 23, 78, 100, 112, 116] [3, 6, 15, 22, 77, 121, 123, 129]
H_Z (70 checks, sparse supports)
[22, 26, 38, 60, 77, 103, 124, 136] [11, 17, 19, 63, 76, 102, 125, 137] [24, 28, 40, 62, 89, 115, 126, 138] [13, 19, 21, 65, 88, 114, 127, 139] [26, 30, 42, 64, 70, 101, 127, 128] [15, 21, 23, 67, 71, 100, 126, 129] [28, 32, 44, 66, 72, 113, 130, 139] [17, 23, 25, 69, 73, 112, 131, 138] [30, 34, 46, 68, 74, 81, 125, 132] [1, 19, 25, 27, 75, 80, 124, 133] [0, 32, 36, 48, 76, 93, 134, 137] [3, 21, 27, 29, 77, 92, 135, 136] [2, 34, 38, 50, 78, 79, 105, 136] [5, 23, 29, 31, 78, 79, 104, 137] [4, 36, 40, 52, 80, 91, 117, 138] [7, 25, 31, 33, 81, 90, 116, 139] [6, 38, 42, 54, 70, 82, 103, 129] [9, 27, 33, 35, 71, 83, 102, 128] [8, 40, 44, 56, 71, 72, 84, 115] [11, 29, 35, 37, 70, 73, 85, 114] [10, 42, 46, 58, 74, 83, 86, 127] [13, 31, 37, 39, 75, 82, 87, 126] [12, 44, 48, 60, 76, 88, 95, 139] [15, 33, 39, 41, 77, 89, 94, 138] [14, 46, 50, 62, 78, 81, 90, 107] [17, 35, 41, 43, 79, 80, 91, 106] [16, 48, 52, 64, 80, 92, 93, 119] [19, 37, 43, 45, 81, 92, 93, 118] [18, 50, 54, 66, 82, 94, 105, 131] [21, 39, 45, 47, 83, 95, 104, 130] [20, 52, 56, 68, 73, 84, 96, 117] [23, 41, 47, 49, 72, 85, 97, 116] [0, 22, 54, 58, 85, 86, 98, 129] [25, 43, 49, 51, 84, 87, 99, 128] [2, 24, 56, 60, 71, 88, 97, 100] [27, 45, 51, 53, 70, 89, 96, 101] [4, 26, 58, 62, 83, 90, 102, 109] [29, 47, 53, 55, 82, 91, 103, 108] [6, 28, 60, 64, 92, 95, 104, 121] [31, 49, 55, 57, 93, 94, 105, 120] [8, 30, 62, 66, 94, 106, 107, 133] [33, 51, 57, 59, 95, 106, 107, 132] [10, 32, 64, 68, 75, 96, 108, 119] [35, 53, 59, 61, 74, 97, 109, 118] [0, 12, 34, 66, 87, 98, 110, 131] [37, 55, 61, 63, 86, 99, 111, 130] [2, 14, 36, 68, 73, 99, 100, 112] [39, 57, 63, 65, 72, 98, 101, 113] [0, 4, 16, 38, 85, 102, 111, 114] [41, 59, 65, 67, 84, 103, 110, 115] [2, 6, 18, 40, 97, 104, 116, 123] [43, 61, 67, 69, 96, 105, 117, 122] [4, 8, 20, 42, 106, 109, 118, 135] [1, 45, 63, 69, 107, 108, 119, 134] [6, 10, 22, 44, 77, 108, 120, 121] [1, 3, 47, 65, 76, 109, 120, 121] [8, 12, 24, 46, 89, 110, 122, 133] [3, 5, 49, 67, 88, 111, 123, 132] [10, 14, 26, 48, 75, 101, 112, 124] [5, 7, 51, 69, 74, 100, 113, 125] [12, 16, 28, 50, 87, 113, 114, 126] [1, 7, 9, 53, 86, 112, 115, 127] [14, 18, 30, 52, 99, 116, 125, 128] [3, 9, 11, 55, 98, 117, 124, 129] [16, 20, 32, 54, 111, 118, 130, 137] [5, 11, 13, 57, 110, 119, 131, 136] [18, 22, 34, 56, 79, 120, 123, 132] [7, 13, 15, 59, 78, 121, 122, 133] [20, 24, 36, 58, 91, 122, 134, 135] [9, 15, 17, 61, 90, 123, 134, 135]
raw submission JSON