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[[190,38,8]] d ≤
n
190
k
38
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)
[82, 85, 92, 99, 102, 108, 137, 140]
d_Z 8 · witness weight 8 (claimed upper_bound)
witness operator (support, 8 qubits)
[3, 22, 23, 78, 80, 81, 83, 95]
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 D19 (order 38): a0=[17, 19, 36], a1=[0, 6, 9], b0=[10, 30, 31], b1=[0, 1, 12] 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 76 · Z-checks 76
H_X (76 checks, sparse supports)
[6, 19, 36, 76, 77, 93, 162, 182, 183] [10, 15, 35, 77, 79, 89, 166, 186, 187] [11, 14, 34, 78, 80, 88, 168, 188, 189] [11, 14, 31, 79, 82, 85, 170, 188, 189] [10, 15, 30, 80, 83, 84, 164, 184, 185] [7, 18, 37, 78, 81, 92, 172, 186, 187] [7, 18, 27, 76, 82, 86, 174, 184, 185] [6, 19, 26, 81, 83, 87, 160, 180, 181] [4, 22, 33, 81, 84, 96, 176, 182, 183] [3, 23, 32, 76, 85, 97, 158, 178, 179] [4, 22, 23, 77, 86, 90, 178, 180, 181] [3, 22, 23, 78, 87, 91, 157, 176, 177] [2, 26, 29, 84, 88, 100, 178, 179, 180] [1, 27, 28, 85, 89, 101, 155, 174, 175] [2, 19, 26, 79, 90, 94, 176, 177, 182] [1, 18, 27, 80, 91, 95, 154, 172, 173] [5, 25, 30, 88, 92, 104, 174, 175, 184] [0, 24, 31, 89, 93, 105, 153, 170, 171] [5, 15, 30, 82, 94, 98, 172, 173, 186] [0, 14, 31, 83, 95, 99, 156, 168, 169] [8, 21, 34, 92, 96, 108, 170, 171, 188] [9, 20, 35, 93, 97, 109, 152, 166, 167] [8, 11, 34, 86, 98, 102, 168, 169, 189] [9, 10, 35, 87, 99, 103, 159, 164, 165] [12, 17, 37, 96, 100, 112, 166, 167, 187] [13, 16, 36, 97, 101, 113, 161, 162, 163] [7, 12, 37, 90, 102, 106, 164, 165, 185] [6, 13, 36, 91, 103, 107, 160, 161, 163] [13, 16, 33, 100, 104, 111, 162, 163, 183] [12, 17, 32, 101, 105, 110, 158, 159, 165] [4, 16, 33, 94, 106, 110, 160, 161, 181] [3, 17, 32, 95, 107, 111, 152, 157, 167] [9, 20, 29, 104, 107, 108, 158, 159, 179] [8, 21, 28, 105, 106, 109, 155, 156, 169] [2, 20, 29, 98, 110, 113, 152, 157, 177] [1, 21, 28, 99, 111, 112, 153, 154, 171] [0, 24, 25, 103, 108, 112, 155, 156, 175] [5, 24, 25, 102, 109, 113, 153, 154, 173] [44, 57, 74, 114, 115, 131, 152, 153, 164] [48, 53, 73, 115, 117, 127, 153, 155, 160] [49, 52, 72, 116, 118, 126, 154, 157, 158] [49, 52, 69, 117, 120, 123, 155, 157, 158] [48, 53, 68, 118, 121, 122, 154, 156, 162] [45, 56, 75, 116, 119, 130, 155, 157, 160] [45, 56, 65, 114, 120, 124, 154, 158, 162] [44, 57, 64, 119, 121, 125, 156, 159, 166] [42, 60, 71, 119, 122, 134, 153, 160, 164] [41, 61, 70, 114, 123, 135, 152, 161, 168] [42, 60, 61, 115, 124, 128, 156, 162, 166] [41, 60, 61, 116, 125, 129, 159, 163, 170] [40, 64, 67, 122, 126, 138, 152, 164, 168] [39, 65, 66, 123, 127, 139, 161, 165, 172] [40, 57, 64, 117, 128, 132, 159, 166, 170] [39, 56, 65, 118, 129, 133, 163, 167, 174] [43, 63, 68, 126, 130, 142, 161, 168, 172] [38, 62, 69, 127, 131, 143, 165, 169, 176] [43, 53, 68, 120, 132, 136, 163, 170, 174] [38, 52, 69, 121, 133, 137, 167, 171, 178] [46, 59, 72, 130, 134, 146, 165, 172, 176] [47, 58, 73, 131, 135, 147, 169, 173, 180] [46, 49, 72, 124, 136, 140, 167, 174, 178] [47, 48, 73, 125, 137, 141, 171, 175, 182] [50, 55, 75, 134, 138, 150, 169, 176, 180] [51, 54, 74, 135, 139, 151, 173, 177, 184] [45, 50, 75, 128, 140, 144, 171, 178, 182] [44, 51, 74, 129, 141, 145, 175, 179, 186] [51, 54, 71, 138, 142, 149, 173, 180, 184] [50, 55, 70, 139, 143, 148, 177, 181, 188] [42, 54, 71, 132, 144, 148, 175, 182, 186] [41, 55, 70, 133, 145, 149, 179, 183, 189] [47, 58, 67, 142, 145, 146, 177, 184, 188] [46, 59, 66, 143, 144, 147, 181, 185, 187] [40, 58, 67, 136, 148, 151, 179, 186, 189] [39, 59, 66, 137, 149, 150, 183, 185, 187] [38, 62, 63, 141, 146, 150, 181, 187, 188] [43, 62, 63, 140, 147, 151, 183, 185, 189]
H_Z (76 checks, sparse supports)
[21, 31, 34, 38, 47, 50, 169, 171, 188] [17, 35, 37, 38, 39, 46, 165, 167, 187] [15, 35, 37, 40, 42, 44, 164, 166, 186] [13, 33, 36, 39, 41, 43, 161, 163, 183] [19, 33, 36, 42, 45, 48, 160, 162, 182] [11, 31, 34, 40, 41, 43, 168, 170, 189] [9, 29, 32, 40, 41, 44, 152, 159, 179] [23, 29, 32, 45, 49, 52, 157, 158, 178] [7, 27, 30, 39, 43, 46, 172, 174, 185] [25, 27, 30, 47, 51, 54, 173, 175, 184] [0, 25, 28, 42, 44, 48, 153, 156, 175] [25, 27, 28, 49, 53, 56, 154, 155, 174] [4, 23, 26, 38, 46, 50, 176, 178, 181] [23, 26, 29, 51, 55, 58, 177, 179, 180] [1, 21, 24, 45, 48, 52, 154, 155, 171] [21, 24, 31, 53, 57, 60, 153, 156, 170] [2, 19, 22, 47, 50, 54, 177, 180, 182] [19, 22, 33, 55, 59, 62, 176, 181, 183] [3, 17, 20, 49, 52, 56, 157, 158, 167] [17, 20, 35, 57, 61, 64, 152, 159, 166] [5, 15, 18, 51, 54, 58, 173, 184, 186] [15, 18, 37, 59, 63, 66, 172, 185, 187] [6, 13, 16, 53, 56, 60, 160, 162, 163] [13, 16, 36, 61, 65, 68, 161, 162, 163] [8, 11, 14, 55, 58, 62, 169, 188, 189] [11, 14, 34, 63, 67, 70, 168, 188, 189] [9, 10, 12, 57, 60, 64, 159, 164, 166] [9, 12, 32, 65, 69, 72, 158, 165, 167] [7, 10, 12, 59, 62, 66, 165, 185, 187] [7, 10, 30, 67, 71, 74, 164, 184, 186] [0, 8, 14, 61, 64, 68, 156, 168, 170] [0, 8, 28, 69, 73, 75, 155, 169, 171] [4, 6, 16, 63, 66, 70, 161, 181, 183] [4, 6, 26, 71, 73, 75, 160, 180, 182] [1, 5, 18, 65, 68, 72, 154, 172, 174] [1, 5, 24, 71, 73, 74, 153, 173, 175] [2, 3, 20, 67, 70, 74, 152, 177, 179] [2, 3, 22, 69, 72, 75, 157, 176, 178] [97, 107, 110, 114, 123, 126, 152, 158, 161] [93, 111, 113, 114, 115, 122, 152, 153, 162] [91, 111, 113, 116, 118, 120, 154, 157, 163] [89, 109, 112, 115, 117, 119, 153, 155, 166] [95, 109, 112, 118, 121, 124, 154, 156, 167] [87, 107, 110, 116, 117, 119, 157, 159, 160] [85, 105, 108, 116, 117, 120, 155, 158, 170] [99, 105, 108, 121, 125, 128, 156, 159, 171] [83, 103, 106, 115, 119, 122, 156, 160, 164] [101, 103, 106, 123, 127, 130, 155, 161, 165] [76, 101, 104, 118, 120, 124, 158, 162, 174] [101, 103, 104, 125, 129, 132, 159, 163, 175] [80, 99, 102, 114, 122, 126, 154, 164, 168] [99, 102, 105, 127, 131, 134, 153, 165, 169] [77, 97, 100, 121, 124, 128, 162, 166, 178] [97, 100, 107, 129, 133, 136, 163, 167, 179] [78, 95, 98, 123, 126, 130, 157, 168, 172] [95, 98, 109, 131, 135, 138, 152, 169, 173] [79, 93, 96, 125, 128, 132, 166, 170, 182] [93, 96, 111, 133, 137, 140, 167, 171, 183] [81, 91, 94, 127, 130, 134, 160, 172, 176] [91, 94, 113, 135, 139, 142, 161, 173, 177] [82, 89, 92, 129, 132, 136, 170, 174, 186] [89, 92, 112, 137, 141, 144, 171, 175, 187] [84, 87, 90, 131, 134, 138, 164, 176, 180] [87, 90, 110, 139, 143, 146, 165, 177, 181] [85, 86, 88, 133, 136, 140, 174, 178, 189] [85, 88, 108, 141, 145, 148, 175, 179, 188] [83, 86, 88, 135, 138, 142, 168, 180, 184] [83, 86, 106, 143, 147, 150, 169, 181, 185] [76, 84, 90, 137, 140, 144, 178, 182, 185] [76, 84, 104, 145, 149, 151, 179, 183, 184] [80, 82, 92, 139, 142, 146, 172, 184, 188] [80, 82, 102, 147, 149, 151, 173, 185, 189] [77, 81, 94, 141, 144, 148, 181, 182, 186] [77, 81, 100, 147, 149, 150, 180, 183, 187] [78, 79, 96, 143, 146, 150, 176, 187, 188] [78, 79, 98, 145, 148, 151, 177, 186, 189]
raw submission JSON