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[[144,6,18]] d ≤
n
144
k
6
d
18
kd²/n
13.5
w
12

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Distance

d_X 18 · witness weight 18 (claimed upper_bound)
witness operator (support, 18 qubits)
[8, 11, 19, 21, 28, 37, 47, 63, 66, 69, 81, 88, 90, 92, 96, 100, 114, 128]
d_Z 18 · witness weight 18 (claimed upper_bound)
witness operator (support, 18 qubits)
[10, 14, 23, 30, 33, 36, 44, 49, 82, 88, 89, 90, 95, 103, 108, 119, 120, 121]
certificate none yet · distance stands as a self-certified upper bound (d ≤)

Construction & provenance

authors @mathysrennela
provenance submitted through the challenge
novelty novelty not audited
construction 2BGA (arXiv:2306.16400) on GAP C36xC2, weight-6 random supports a=[10, 17, 28, 45, 51, 58] b=[1, 7, 11, 16, 26, 70]
model Xiaomi MiMo-V2.5 (claimed, not verified)
builds on arXiv:2306.16400
date 2026-07-29
notes Found by GAP-enhanced autoresearch (see fieldnotes/2026-07-28-gap-campaign-results.md). 2BGA code on C36xC2, weight-6 random supports. Distance upper bound confirmed flat across 400->1M RIS trials. Literature novelty unverified.
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 72 · Z-checks 72
H_X (72 checks, sparse supports)
[5, 9, 20, 33, 47, 63, 80, 83, 99, 107, 121, 141] [9, 16, 29, 43, 55, 67, 72, 91, 109, 117, 124, 129] [9, 12, 20, 32, 48, 52, 76, 86, 91, 106, 122, 143] [2, 15, 23, 30, 38, 51, 80, 94, 99, 118, 125, 135] [15, 16, 24, 39, 62, 70, 73, 74, 82, 89, 132, 136] [17, 25, 26, 40, 53, 63, 76, 82, 96, 101, 113, 120] [16, 20, 29, 42, 56, 60, 74, 80, 94, 116, 130, 135] [6, 23, 33, 40, 48, 59, 72, 75, 109, 126, 133, 139] [5, 12, 23, 24, 66, 71, 76, 78, 90, 97, 137, 140] [25, 35, 36, 50, 61, 67, 77, 80, 85, 90, 111, 128] [0, 17, 23, 28, 38, 62, 86, 91, 103, 109, 124, 136] [24, 28, 29, 39, 51, 65, 72, 75, 78, 102, 125, 139] [13, 25, 30, 40, 52, 64, 75, 83, 88, 105, 111, 126] [10, 32, 35, 42, 49, 55, 74, 94, 101, 113, 118, 137] [11, 32, 33, 43, 50, 56, 73, 79, 82, 98, 106, 142] [2, 12, 34, 44, 57, 65, 86, 96, 98, 115, 120, 134] [34, 35, 45, 46, 58, 70, 72, 81, 84, 93, 99, 100] [0, 1, 6, 14, 26, 47, 88, 100, 117, 122, 131, 136] [1, 25, 33, 38, 48, 66, 74, 82, 94, 113, 132, 140] [5, 12, 38, 39, 59, 69, 73, 79, 83, 112, 133, 142] [21, 35, 40, 50, 60, 68, 79, 84, 91, 96, 98, 115] [18, 42, 45, 51, 57, 62, 75, 78, 85, 111, 126, 141] [15, 19, 28, 42, 43, 58, 76, 86, 90, 108, 116, 143] [6, 20, 44, 53, 64, 69, 77, 87, 94, 108, 128, 138] [17, 30, 44, 45, 54, 71, 73, 88, 92, 103, 109, 110] [1, 4, 11, 22, 36, 55, 89, 96, 104, 110, 130, 140] [3, 34, 42, 47, 50, 55, 72, 88, 103, 109, 126, 142] [4, 35, 43, 47, 48, 56, 75, 78, 85, 90, 121, 137] [0, 5, 44, 49, 57, 70, 85, 99, 105, 111, 123, 128] [31, 45, 49, 50, 58, 65, 74, 77, 86, 87, 92, 108] [1, 2, 6, 13, 27, 32, 87, 101, 107, 125, 130, 138] [17, 27, 51, 59, 64, 66, 79, 83, 84, 93, 98, 124] [4, 10, 28, 52, 60, 67, 84, 103, 115, 122, 131, 134] [11, 29, 52, 53, 61, 68, 75, 81, 95, 100, 118, 119] [3, 7, 12, 18, 30, 31, 105, 117, 119, 133, 136, 142] [3, 4, 8, 19, 46, 62, 77, 97, 102, 114, 120, 121] [7, 44, 51, 55, 58, 62, 73, 82, 96, 98, 113, 143] [8, 15, 28, 45, 55, 56, 79, 83, 93, 99, 129, 141] [1, 9, 53, 57, 64, 71, 84, 93, 100, 109, 115, 131] [17, 30, 41, 57, 58, 69, 78, 81, 94, 95, 101, 118] [4, 6, 11, 21, 37, 42, 95, 102, 111, 117, 119, 133] [25, 32, 37, 47, 59, 68, 86, 91, 92, 103, 108, 132] [8, 18, 38, 60, 65, 70, 87, 92, 104, 113, 130, 138] [19, 34, 39, 49, 60, 61, 79, 88, 105, 110, 126, 127] [7, 14, 20, 27, 40, 41, 89, 106, 115, 127, 140, 143] [0, 2, 7, 8, 54, 66, 81, 107, 112, 123, 128, 129] [14, 30, 53, 59, 62, 66, 76, 77, 85, 90, 108, 135] [3, 11, 15, 60, 63, 67, 77, 107, 118, 123, 128, 138] [4, 16, 61, 63, 64, 68, 82, 87, 92, 103, 104, 110] [5, 7, 10, 17, 18, 46, 104, 120, 125, 130, 137, 140] [8, 10, 11, 19, 31, 51, 84, 89, 105, 106, 112, 127] [0, 27, 48, 65, 69, 71, 85, 95, 101, 102, 114, 119] [13, 16, 21, 28, 36, 49, 83, 102, 123, 133, 141, 142] [13, 14, 22, 29, 37, 50, 87, 97, 116, 121, 134, 135] [22, 32, 40, 47, 61, 66, 80, 81, 93, 99, 118, 139] [7, 19, 23, 65, 67, 70, 81, 100, 117, 119, 126, 131] [8, 24, 34, 49, 67, 68, 90, 95, 101, 113, 114, 120] [9, 14, 18, 25, 27, 54, 102, 114, 121, 128, 133, 141] [0, 2, 18, 19, 41, 59, 92, 97, 115, 116, 122, 134] [1, 37, 52, 56, 63, 69, 93, 105, 111, 112, 123, 127] [21, 24, 31, 38, 46, 57, 91, 106, 112, 124, 131, 143] [3, 10, 21, 22, 39, 58, 95, 107, 125, 129, 138, 139] [2, 14, 33, 69, 70, 71, 88, 89, 98, 104, 110, 127] [15, 21, 26, 29, 34, 36, 76, 89, 134, 137, 140, 143] [16, 22, 26, 27, 35, 37, 100, 106, 112, 123, 124, 129] [5, 31, 41, 48, 54, 64, 74, 104, 116, 122, 132, 135] [6, 22, 43, 52, 63, 71, 96, 97, 108, 114, 120, 134] [23, 31, 36, 39, 44, 46, 80, 97, 121, 135, 138, 141] [3, 10, 24, 36, 37, 45, 110, 116, 122, 131, 132, 136] [9, 13, 26, 41, 56, 68, 78, 114, 125, 130, 137, 139] [12, 33, 41, 46, 53, 54, 72, 107, 119, 124, 129, 139] [13, 20, 26, 43, 54, 61, 73, 117, 127, 132, 136, 142]
H_Z (72 checks, sparse supports)
[1, 7, 11, 16, 26, 70, 82, 89, 100, 117, 123, 130] [4, 14, 19, 24, 36, 71, 89, 90, 97, 102, 110, 131] [4, 6, 13, 18, 29, 65, 75, 87, 102, 117, 130, 134] [7, 11, 12, 21, 27, 33, 98, 106, 107, 119, 133, 140] [2, 5, 8, 22, 46, 63, 97, 99, 104, 107, 112, 120] [9, 23, 29, 35, 46, 47, 72, 80, 91, 100, 121, 137] [8, 11, 21, 27, 39, 69, 79, 89, 95, 102, 112, 138] [14, 19, 20, 31, 37, 43, 106, 108, 116, 117, 121, 127] [0, 3, 6, 9, 54, 67, 107, 109, 114, 117, 122, 128] [16, 33, 39, 45, 54, 55, 72, 73, 74, 110, 129, 141] [4, 5, 14, 18, 36, 48, 85, 104, 121, 122, 133, 140] [0, 12, 19, 31, 37, 52, 86, 97, 105, 112, 119, 122] [16, 20, 31, 32, 38, 50, 74, 80, 87, 91, 106, 142] [9, 21, 27, 28, 46, 51, 84, 102, 124, 125, 141, 143] [2, 10, 15, 22, 29, 41, 89, 116, 118, 125, 129, 134] [23, 29, 30, 42, 48, 53, 75, 76, 94, 109, 119, 135] [12, 17, 24, 26, 43, 62, 73, 76, 78, 120, 124, 136] [4, 25, 44, 50, 62, 63, 77, 82, 96, 103, 111, 121] [8, 9, 22, 27, 46, 56, 93, 106, 114, 121, 129, 130] [1, 2, 10, 20, 41, 60, 94, 107, 115, 122, 127, 130] [24, 29, 41, 42, 48, 58, 72, 74, 78, 95, 116, 143] [16, 31, 37, 38, 54, 59, 92, 112, 124, 132, 133, 135] [3, 6, 13, 18, 23, 39, 97, 125, 126, 133, 136, 138] [33, 39, 40, 51, 56, 61, 75, 79, 80, 82, 127, 139] [5, 15, 20, 25, 36, 66, 76, 80, 83, 128, 132, 140] [8, 35, 53, 58, 66, 67, 77, 81, 84, 90, 113, 129] [14, 15, 20, 31, 36, 62, 77, 89, 135, 136, 141, 143] [0, 3, 16, 28, 37, 54, 102, 103, 116, 123, 129, 136] [16, 17, 33, 38, 55, 64, 82, 83, 94, 104, 109, 124] [5, 13, 30, 39, 51, 56, 73, 78, 83, 105, 125, 135] [11, 35, 40, 51, 52, 57, 75, 84, 96, 106, 111, 118] [10, 24, 26, 32, 41, 48, 101, 106, 122, 132, 137, 139] [25, 42, 48, 49, 62, 65, 74, 85, 86, 102, 113, 126] [12, 28, 34, 43, 50, 59, 72, 79, 86, 90, 134, 142] [2, 14, 44, 50, 60, 64, 87, 88, 98, 115, 128, 135] [0, 30, 45, 47, 61, 70, 81, 85, 88, 92, 99, 136] [22, 23, 29, 41, 46, 66, 81, 97, 124, 135, 139, 140] [1, 7, 10, 24, 26, 38, 112, 113, 125, 131, 136, 140] [24, 25, 43, 48, 62, 68, 75, 82, 90, 91, 114, 132] [9, 12, 21, 28, 40, 59, 76, 83, 91, 115, 133, 139] [19, 45, 50, 59, 60, 64, 77, 79, 84, 92, 116, 126] [5, 13, 18, 36, 42, 56, 111, 116, 130, 137, 141, 142] [35, 51, 56, 57, 66, 69, 78, 85, 93, 94, 98, 112] [15, 20, 32, 38, 44, 58, 73, 86, 94, 99, 138, 143] [6, 22, 53, 58, 65, 68, 87, 95, 96, 100, 108, 139] [1, 17, 34, 40, 55, 71, 88, 93, 96, 101, 109, 140] [3, 13, 33, 39, 47, 54, 88, 107, 121, 132, 139, 142] [33, 34, 40, 51, 55, 70, 72, 89, 98, 99, 113, 126] [5, 15, 35, 49, 56, 66, 74, 79, 90, 99, 123, 137] [0, 27, 35, 53, 57, 67, 85, 100, 101, 115, 124, 128] [2, 17, 32, 58, 65, 68, 81, 86, 92, 98, 101, 125] [28, 45, 47, 52, 59, 64, 75, 83, 93, 103, 108, 122] [1, 10, 31, 60, 64, 70, 74, 84, 104, 105, 131, 138] [3, 11, 30, 49, 61, 69, 77, 95, 105, 110, 118, 142] [7, 12, 21, 26, 43, 55, 96, 117, 129, 137, 142, 143] [43, 44, 50, 59, 62, 71, 73, 85, 97, 98, 108, 109] [9, 23, 28, 45, 47, 57, 78, 86, 99, 109, 131, 141] [1, 37, 45, 61, 64, 70, 87, 93, 100, 110, 111, 132] [6, 25, 30, 42, 49, 69, 88, 94, 101, 108, 111, 133] [17, 32, 38, 55, 60, 68, 79, 91, 103, 113, 118, 130] [4, 18, 41, 65, 68, 71, 78, 92, 104, 114, 115, 119] [7, 19, 34, 40, 52, 57, 81, 105, 115, 120, 126, 143] [15, 32, 53, 58, 63, 66, 76, 82, 93, 107, 108, 118] [3, 6, 46, 53, 65, 67, 72, 77, 119, 120, 131, 138] [4, 10, 17, 34, 68, 71, 84, 95, 103, 110, 120, 137] [8, 13, 27, 49, 63, 69, 83, 87, 101, 114, 123, 127] [23, 30, 42, 47, 61, 67, 80, 90, 103, 117, 118, 126] [7, 11, 54, 61, 69, 70, 73, 81, 104, 119, 127, 128] [8, 18, 25, 44, 49, 63, 92, 105, 113, 120, 128, 141] [0, 21, 37, 52, 57, 67, 91, 95, 111, 123, 131, 134] [14, 19, 26, 34, 52, 71, 76, 88, 100, 114, 127, 134] [2, 22, 36, 44, 60, 63, 80, 96, 110, 123, 134, 138]
raw submission JSON