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[[170,34,8]] d ≤
n
170
k
34
d
8
kd²/n
12.8
w
9

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Distance

d_X 8 · witness weight 8 (claimed upper_bound)
witness operator (support, 8 qubits)
[68, 88, 102, 116, 120, 122, 125, 129]
d_Z 8 · witness weight 8 (claimed upper_bound)
witness operator (support, 8 qubits)
[38, 41, 44, 48, 63, 65, 115, 122]
certificate none yet · distance stands as a self-certified upper bound (d ≤)

Construction & provenance

authors @yhu1996
provenance submitted through the challenge
novelty novelty not audited
construction Mitten lifted product LP(A,B) (Bhardwaj et al arXiv:2607.28795, Def.4/8) on non-abelian group D17 (order 34): a0=[3, 5, 6], a1=[0, 13, 26], b0=[19, 22, 25], b1=[0, 4, 20] over F2[G]. n=5|G|, k=|G|, weight-9.
model Claude Claude Opus 4.8 (claimed, not verified)
builds on arXiv:2607.28795
date 2026-08-04
notes Found with Jukebox
family lifted product (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 68 · Z-checks 68
H_X (68 checks, sparse supports)
[5, 13, 17, 68, 71, 98, 155, 158, 161] [8, 9, 13, 69, 74, 101, 157, 159, 162] [8, 9, 12, 70, 75, 100, 155, 161, 164] [0, 9, 12, 71, 78, 97, 153, 163, 166] [5, 8, 13, 72, 79, 96, 157, 159, 160] [0, 12, 16, 72, 73, 99, 151, 165, 168] [0, 1, 16, 74, 82, 93, 149, 167, 169] [2, 5, 17, 75, 83, 92, 153, 156, 163] [1, 16, 20, 70, 76, 95, 147, 167, 169] [2, 17, 21, 69, 77, 94, 151, 154, 165] [1, 3, 20, 78, 86, 89, 145, 165, 168] [2, 4, 21, 79, 87, 88, 149, 152, 167] [3, 20, 24, 73, 80, 91, 143, 163, 166] [4, 21, 25, 68, 81, 90, 147, 150, 169] [3, 6, 24, 82, 85, 90, 136, 161, 164] [4, 7, 25, 83, 84, 91, 145, 148, 168] [6, 24, 28, 76, 84, 87, 140, 159, 162] [7, 25, 29, 77, 85, 86, 143, 146, 166] [6, 10, 28, 81, 86, 94, 137, 157, 160] [7, 11, 29, 80, 87, 95, 136, 144, 164] [10, 28, 32, 80, 83, 88, 138, 155, 158] [11, 29, 33, 81, 82, 89, 140, 142, 162] [10, 14, 32, 77, 90, 98, 139, 153, 156] [11, 15, 33, 76, 91, 99, 137, 141, 160] [14, 31, 32, 79, 84, 92, 141, 151, 154] [15, 30, 33, 78, 85, 93, 138, 139, 158] [14, 18, 31, 68, 94, 101, 142, 149, 152] [15, 19, 30, 73, 95, 100, 138, 139, 156] [18, 27, 31, 75, 88, 96, 144, 147, 150] [19, 26, 30, 74, 89, 97, 137, 141, 154] [18, 22, 27, 69, 97, 98, 145, 146, 148] [19, 23, 26, 70, 96, 99, 140, 142, 152] [22, 23, 27, 72, 92, 100, 143, 146, 148] [22, 23, 26, 71, 93, 101, 136, 144, 150] [39, 47, 51, 102, 105, 132, 136, 140, 156] [42, 43, 47, 103, 108, 135, 137, 143, 152] [42, 43, 46, 104, 109, 134, 138, 145, 150] [34, 43, 46, 105, 112, 131, 139, 147, 148] [39, 42, 47, 106, 113, 130, 136, 140, 154] [34, 46, 50, 106, 107, 133, 141, 146, 149] [34, 35, 50, 108, 116, 127, 142, 144, 151] [36, 39, 51, 109, 117, 126, 137, 143, 158] [35, 50, 54, 104, 110, 129, 142, 144, 153] [36, 51, 55, 103, 111, 128, 138, 145, 160] [35, 37, 54, 112, 120, 123, 141, 146, 155] [36, 38, 55, 113, 121, 122, 139, 147, 162] [37, 54, 58, 107, 114, 125, 139, 148, 157] [38, 55, 59, 102, 115, 124, 141, 149, 164] [37, 40, 58, 116, 119, 124, 138, 150, 159] [38, 41, 59, 117, 118, 125, 142, 151, 166] [40, 58, 62, 110, 118, 121, 137, 152, 161] [41, 59, 63, 111, 119, 120, 144, 153, 168] [40, 44, 62, 115, 120, 128, 140, 154, 163] [41, 45, 63, 114, 121, 129, 146, 155, 169] [44, 62, 66, 114, 117, 122, 136, 156, 165] [45, 63, 67, 115, 116, 123, 148, 157, 167] [44, 48, 66, 111, 124, 132, 143, 158, 167] [45, 49, 67, 110, 125, 133, 150, 159, 165] [48, 65, 66, 113, 118, 126, 145, 160, 169] [49, 64, 67, 112, 119, 127, 152, 161, 163] [48, 52, 65, 102, 128, 135, 147, 162, 168] [49, 53, 64, 107, 129, 134, 154, 161, 163] [52, 61, 65, 109, 122, 130, 149, 164, 166] [53, 60, 64, 108, 123, 131, 156, 159, 165] [52, 56, 61, 103, 131, 132, 151, 164, 166] [53, 57, 60, 104, 130, 133, 157, 158, 167] [56, 57, 61, 106, 126, 134, 153, 162, 168] [56, 57, 60, 105, 127, 135, 155, 160, 169]
H_Z (68 checks, sparse supports)
[14, 19, 33, 34, 38, 54, 139, 141, 142] [18, 23, 29, 35, 41, 50, 142, 144, 146] [20, 25, 27, 36, 43, 48, 143, 145, 147] [22, 25, 27, 37, 45, 46, 146, 148, 150] [16, 21, 31, 34, 38, 52, 147, 149, 151] [23, 24, 29, 39, 44, 47, 136, 140, 143] [21, 26, 31, 40, 42, 49, 150, 152, 154] [12, 17, 32, 35, 41, 56, 151, 153, 155] [19, 28, 33, 40, 42, 51, 137, 138, 140] [10, 15, 30, 36, 43, 58, 137, 138, 139] [17, 30, 32, 39, 44, 53, 154, 156, 158] [8, 13, 28, 37, 45, 60, 155, 157, 159] [15, 30, 32, 37, 46, 55, 138, 139, 141] [6, 11, 26, 39, 47, 62, 136, 137, 140] [13, 28, 33, 36, 48, 57, 158, 160, 162] [5, 9, 24, 40, 49, 64, 159, 161, 163] [11, 26, 31, 35, 50, 59, 141, 142, 144] [3, 7, 22, 42, 51, 66, 136, 143, 145] [9, 24, 29, 38, 52, 61, 162, 164, 166] [0, 2, 20, 44, 53, 67, 163, 165, 167] [7, 22, 27, 34, 54, 63, 144, 146, 148] [1, 4, 18, 46, 55, 65, 145, 147, 149] [0, 20, 25, 41, 56, 65, 166, 168, 169] [1, 4, 16, 48, 57, 63, 167, 168, 169] [4, 18, 23, 43, 58, 67, 148, 150, 152] [0, 2, 14, 50, 59, 61, 149, 151, 153] [1, 16, 21, 45, 60, 66, 165, 167, 169] [3, 7, 12, 52, 59, 61, 164, 166, 168] [2, 14, 19, 47, 62, 64, 152, 154, 156] [5, 9, 10, 54, 57, 63, 153, 155, 157] [3, 12, 17, 49, 62, 64, 161, 163, 165] [6, 8, 11, 55, 56, 65, 160, 162, 164] [5, 10, 15, 51, 60, 66, 156, 158, 160] [6, 8, 13, 53, 58, 67, 157, 159, 161] [82, 87, 101, 102, 106, 122, 136, 149, 162] [86, 91, 97, 103, 109, 118, 137, 145, 166] [88, 93, 95, 104, 111, 116, 138, 144, 167] [90, 93, 95, 105, 113, 114, 136, 139, 169] [84, 89, 99, 102, 106, 120, 140, 141, 168] [91, 92, 97, 107, 112, 115, 141, 148, 163] [89, 94, 99, 108, 110, 117, 137, 142, 165] [80, 85, 100, 103, 109, 124, 138, 143, 164] [87, 96, 101, 108, 110, 119, 144, 152, 159] [78, 83, 98, 104, 111, 126, 145, 153, 158] [85, 98, 100, 107, 112, 121, 139, 146, 161] [76, 81, 96, 105, 113, 128, 140, 147, 160] [83, 98, 100, 105, 114, 123, 148, 155, 156] [74, 79, 94, 107, 115, 130, 149, 154, 157] [81, 96, 101, 104, 116, 125, 142, 150, 157] [73, 77, 92, 108, 117, 132, 143, 151, 156] [79, 94, 99, 103, 118, 127, 151, 152, 160] [71, 75, 90, 110, 119, 134, 150, 153, 161] [77, 92, 97, 106, 120, 129, 146, 153, 154] [68, 70, 88, 112, 121, 135, 147, 152, 155] [75, 90, 95, 102, 122, 131, 147, 156, 164] [69, 72, 86, 114, 123, 133, 146, 157, 165] [68, 88, 93, 109, 124, 133, 149, 150, 158] [69, 72, 84, 116, 125, 131, 148, 151, 159] [72, 86, 91, 111, 126, 135, 143, 160, 168] [68, 70, 82, 118, 127, 129, 142, 161, 169] [69, 84, 89, 113, 128, 134, 145, 154, 162] [71, 75, 80, 120, 127, 129, 144, 155, 163] [70, 82, 87, 115, 130, 132, 140, 164, 167] [73, 77, 78, 122, 125, 131, 139, 165, 166] [71, 80, 85, 117, 130, 132, 136, 158, 166] [74, 76, 79, 123, 124, 133, 141, 159, 167] [73, 78, 83, 119, 128, 134, 138, 163, 168] [74, 76, 81, 121, 126, 135, 137, 162, 169]
raw submission JSON