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[[132,6,17]] d ≤
n
132
k
6
d
17
kd²/n
13.136
w
12

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Distance

d_X 17 · witness weight 17 (claimed upper_bound)
witness operator (support, 17 qubits)
[0, 7, 9, 10, 23, 32, 44, 48, 60, 62, 70, 80, 90, 96, 97, 108, 112]
d_Z 17 · witness weight 17 (claimed upper_bound)
witness operator (support, 17 qubits)
[11, 35, 44, 48, 60, 61, 64, 69, 71, 79, 87, 96, 97, 99, 108, 109, 124]
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 C66, weight-6 random supports a=[23, 27, 28, 34, 48, 50] b=[4, 14, 37, 50, 54, 64]
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 C66, 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 66 · Z-checks 66
H_X (66 checks, sparse supports)
[8, 25, 41, 45, 51, 52, 73, 74, 75, 85, 102, 110] [11, 28, 38, 42, 48, 49, 72, 76, 77, 88, 105, 113] [13, 30, 35, 41, 46, 57, 67, 78, 79, 90, 92, 115] [14, 31, 47, 51, 57, 58, 79, 80, 81, 91, 108, 116] [16, 32, 33, 38, 43, 54, 66, 81, 82, 93, 95, 118] [17, 34, 44, 48, 54, 55, 78, 82, 83, 94, 111, 119] [18, 20, 40, 46, 47, 51, 69, 70, 80, 84, 97, 120] [19, 36, 41, 47, 52, 62, 71, 84, 85, 96, 98, 121] [20, 37, 53, 57, 62, 63, 85, 86, 87, 97, 114, 122] [21, 23, 37, 43, 44, 48, 68, 71, 83, 87, 100, 123] [22, 38, 39, 44, 49, 60, 69, 87, 88, 99, 101, 124] [23, 40, 50, 54, 60, 61, 84, 88, 89, 100, 117, 125] [24, 26, 46, 52, 53, 57, 74, 76, 86, 90, 103, 126] [25, 42, 47, 53, 58, 65, 77, 90, 91, 102, 104, 127] [4, 26, 43, 59, 62, 65, 66, 91, 92, 93, 103, 120] [27, 29, 43, 49, 50, 54, 73, 77, 89, 93, 106, 128] [28, 44, 45, 50, 55, 64, 74, 93, 94, 105, 107, 129] [2, 29, 46, 56, 60, 64, 67, 90, 94, 95, 106, 123] [30, 32, 52, 58, 59, 62, 80, 82, 92, 96, 109, 130] [9, 31, 48, 53, 59, 63, 68, 83, 96, 97, 108, 110] [1, 9, 10, 32, 49, 65, 69, 97, 98, 99, 109, 126] [33, 35, 49, 55, 56, 60, 79, 83, 95, 99, 112, 131] [6, 34, 50, 51, 56, 61, 70, 80, 99, 100, 111, 113] [0, 6, 7, 35, 52, 64, 71, 96, 100, 101, 112, 128] [1, 36, 38, 58, 63, 65, 72, 86, 88, 98, 102, 115] [1, 4, 15, 37, 54, 59, 73, 89, 102, 103, 114, 116] [5, 9, 15, 16, 38, 55, 74, 103, 104, 105, 115, 130] [0, 39, 41, 55, 61, 64, 75, 85, 89, 101, 105, 118] [0, 2, 12, 40, 56, 57, 76, 86, 105, 106, 117, 119] [3, 6, 12, 13, 41, 58, 77, 102, 106, 107, 118, 131] [4, 5, 9, 42, 44, 63, 78, 92, 94, 104, 108, 121] [1, 5, 10, 21, 43, 60, 79, 95, 108, 109, 120, 122] [11, 15, 21, 22, 44, 61, 72, 80, 109, 110, 111, 121] [2, 3, 6, 45, 47, 61, 81, 91, 95, 107, 111, 124] [0, 3, 7, 18, 46, 62, 82, 92, 111, 112, 123, 125] [8, 12, 18, 19, 47, 63, 75, 83, 108, 112, 113, 124] [4, 10, 11, 15, 48, 50, 84, 98, 100, 110, 114, 127] [5, 11, 16, 27, 49, 64, 66, 85, 101, 114, 115, 126] [2, 17, 21, 27, 28, 50, 78, 86, 115, 116, 117, 127] [2, 7, 8, 12, 51, 53, 87, 97, 101, 113, 117, 129] [3, 8, 13, 24, 52, 65, 67, 88, 98, 117, 118, 128] [4, 14, 18, 24, 25, 53, 81, 89, 114, 118, 119, 129] [10, 16, 17, 21, 54, 56, 68, 90, 104, 106, 116, 120] [6, 11, 17, 22, 33, 55, 69, 91, 107, 120, 121, 130] [7, 23, 27, 33, 34, 56, 68, 84, 92, 121, 122, 123] [7, 13, 14, 18, 57, 59, 70, 93, 103, 107, 119, 123] [8, 9, 14, 19, 30, 58, 71, 94, 104, 123, 124, 131] [10, 20, 24, 30, 31, 59, 70, 87, 95, 120, 124, 125] [0, 16, 22, 23, 27, 60, 73, 96, 110, 112, 122, 126] [12, 17, 23, 28, 39, 61, 72, 74, 97, 113, 126, 127] [0, 13, 29, 33, 39, 40, 66, 73, 90, 98, 127, 128] [1, 13, 19, 20, 24, 62, 76, 99, 109, 113, 125, 128] [14, 15, 20, 25, 36, 63, 75, 77, 100, 110, 128, 129] [1, 16, 26, 30, 36, 37, 67, 76, 93, 101, 126, 129] [3, 22, 28, 29, 33, 64, 66, 79, 102, 116, 118, 130] [2, 18, 23, 29, 34, 45, 68, 78, 80, 103, 119, 130] [3, 19, 35, 39, 45, 46, 68, 69, 79, 96, 104, 131] [5, 19, 25, 26, 30, 65, 67, 82, 105, 115, 119, 131] [4, 20, 21, 26, 31, 42, 70, 81, 83, 106, 116, 131] [5, 22, 32, 36, 42, 43, 70, 71, 82, 99, 107, 130] [6, 8, 28, 34, 35, 39, 69, 72, 85, 108, 122, 124] [7, 24, 29, 35, 40, 51, 72, 73, 84, 86, 109, 125] [9, 11, 25, 31, 32, 36, 71, 75, 88, 111, 121, 125] [10, 26, 27, 32, 37, 48, 75, 76, 87, 89, 112, 122] [12, 14, 34, 40, 41, 45, 66, 74, 78, 91, 114, 129] [15, 17, 31, 37, 38, 42, 67, 77, 81, 94, 117, 127]
H_Z (66 checks, sparse supports)
[4, 14, 37, 50, 54, 64, 89, 93, 94, 100, 114, 116] [2, 17, 40, 53, 57, 65, 86, 90, 91, 97, 117, 119] [9, 19, 42, 44, 55, 56, 83, 94, 99, 104, 105, 121] [6, 10, 20, 43, 56, 60, 95, 99, 100, 106, 120, 122] [6, 22, 45, 47, 58, 59, 80, 91, 96, 102, 107, 124] [7, 9, 23, 46, 59, 62, 92, 96, 97, 103, 123, 125] [1, 24, 32, 49, 60, 61, 88, 89, 95, 99, 109, 126] [0, 15, 25, 48, 50, 61, 89, 100, 105, 110, 111, 127] [0, 12, 16, 26, 49, 64, 66, 101, 105, 106, 112, 126] [0, 27, 35, 52, 62, 63, 85, 86, 92, 96, 112, 128] [1, 12, 28, 51, 53, 63, 86, 97, 102, 108, 113, 129] [1, 13, 15, 29, 52, 65, 67, 98, 102, 103, 109, 128] [2, 5, 30, 38, 55, 64, 94, 95, 101, 105, 115, 130] [2, 3, 21, 31, 54, 56, 68, 95, 106, 111, 116, 117] [3, 6, 18, 22, 32, 55, 69, 107, 111, 112, 118, 130] [3, 4, 33, 41, 58, 65, 91, 92, 98, 102, 118, 131] [4, 5, 18, 34, 57, 59, 70, 92, 103, 108, 114, 119] [5, 9, 19, 21, 35, 58, 71, 104, 108, 109, 115, 131] [6, 7, 11, 36, 44, 61, 72, 100, 101, 107, 111, 121] [0, 7, 8, 27, 37, 60, 73, 101, 112, 117, 122, 123] [8, 12, 24, 28, 38, 61, 72, 74, 113, 117, 118, 124] [8, 9, 10, 39, 47, 63, 75, 97, 98, 104, 108, 124] [1, 10, 11, 24, 40, 62, 76, 98, 109, 114, 120, 125] [11, 15, 25, 27, 41, 63, 75, 77, 110, 114, 115, 121] [2, 12, 13, 17, 42, 50, 78, 106, 107, 113, 117, 127] [3, 13, 14, 33, 43, 64, 66, 79, 107, 118, 123, 128] [2, 14, 18, 30, 34, 44, 78, 80, 119, 123, 124, 129] [4, 14, 15, 16, 45, 53, 81, 103, 104, 110, 114, 129] [5, 16, 17, 30, 46, 65, 67, 82, 104, 115, 120, 126] [4, 17, 21, 31, 33, 47, 81, 83, 116, 120, 121, 127] [7, 18, 19, 23, 48, 56, 68, 84, 112, 113, 119, 123] [6, 8, 19, 20, 39, 49, 69, 85, 113, 124, 128, 131] [7, 20, 24, 36, 40, 50, 70, 84, 86, 125, 128, 129] [10, 20, 21, 22, 51, 59, 70, 87, 109, 110, 116, 120] [9, 11, 22, 23, 36, 52, 71, 88, 110, 121, 126, 130] [10, 23, 27, 37, 39, 53, 68, 87, 89, 122, 126, 127] [0, 13, 24, 25, 29, 54, 73, 90, 118, 119, 125, 128] [12, 14, 25, 26, 45, 55, 74, 75, 91, 119, 129, 131] [13, 26, 30, 42, 46, 56, 67, 70, 76, 90, 92, 131] [1, 16, 26, 27, 28, 57, 76, 93, 115, 116, 122, 126] [15, 17, 28, 29, 42, 58, 72, 77, 94, 116, 127, 130] [16, 29, 33, 43, 45, 59, 66, 68, 73, 93, 95, 130] [3, 19, 30, 31, 35, 60, 67, 79, 96, 124, 125, 131] [18, 20, 31, 32, 51, 61, 70, 75, 80, 81, 97, 125] [0, 19, 32, 36, 48, 52, 71, 75, 76, 82, 96, 98] [5, 22, 32, 33, 34, 62, 66, 82, 99, 121, 122, 130] [21, 23, 34, 35, 48, 63, 68, 72, 78, 83, 100, 122] [1, 22, 35, 39, 49, 51, 69, 72, 73, 79, 99, 101] [8, 25, 36, 37, 41, 64, 67, 71, 75, 85, 102, 129] [2, 24, 26, 37, 38, 57, 67, 76, 81, 86, 87, 103] [3, 25, 38, 42, 54, 58, 77, 81, 82, 88, 102, 104] [11, 28, 38, 39, 40, 65, 66, 69, 72, 88, 105, 127] [4, 27, 29, 40, 41, 54, 66, 73, 78, 84, 89, 106] [5, 28, 41, 45, 55, 57, 74, 78, 79, 85, 105, 107] [6, 14, 31, 42, 43, 47, 70, 71, 77, 81, 91, 108] [7, 30, 32, 43, 44, 62, 71, 82, 87, 92, 93, 109] [8, 31, 44, 48, 60, 63, 83, 87, 88, 94, 108, 110] [9, 17, 34, 44, 45, 46, 68, 69, 74, 78, 94, 111] [10, 33, 35, 46, 47, 60, 69, 79, 84, 90, 95, 112] [11, 34, 47, 51, 61, 62, 80, 84, 85, 91, 111, 113] [12, 20, 37, 48, 49, 53, 76, 77, 83, 87, 97, 114] [13, 36, 38, 49, 50, 65, 77, 88, 93, 98, 99, 115] [15, 23, 40, 50, 51, 52, 73, 74, 80, 84, 100, 117] [16, 39, 41, 52, 53, 64, 74, 85, 90, 96, 101, 118] [18, 26, 43, 54, 55, 59, 82, 83, 89, 93, 103, 120] [21, 29, 46, 56, 57, 58, 79, 80, 86, 90, 106, 123]
raw submission JSON