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[[195,39,8]] d ≤
n
195
k
39
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)
[11, 36, 58, 59, 85, 105, 171, 181]
d_Z 8 · witness weight 8 (claimed upper_bound)
witness operator (support, 8 qubits)
[56, 58, 69, 73, 121, 134, 145, 154]
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 metacyclic(C13:C3,r=3) (order 39): a0=[2, 16, 20], a1=[0, 15, 35], b0=[5, 22, 26], b1=[0, 6, 9] 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 78 · Z-checks 78
H_X (78 checks, sparse supports)
[1, 23, 25, 78, 97, 102, 161, 178, 182] [2, 21, 26, 79, 98, 103, 165, 182, 189] [0, 22, 24, 80, 96, 104, 178, 184, 189] [10, 11, 34, 81, 105, 106, 164, 181, 185] [9, 11, 35, 82, 106, 107, 168, 185, 192] [9, 10, 33, 83, 105, 107, 181, 187, 192] [4, 19, 38, 84, 108, 115, 167, 184, 188] [5, 20, 36, 85, 109, 116, 156, 171, 188] [3, 18, 37, 86, 110, 114, 156, 184, 190] [13, 26, 28, 85, 87, 111, 170, 187, 191] [14, 24, 29, 86, 88, 112, 159, 174, 191] [12, 25, 27, 84, 89, 113, 159, 187, 193] [14, 22, 37, 90, 94, 114, 173, 190, 194] [12, 23, 38, 91, 95, 115, 162, 177, 194] [13, 21, 36, 92, 93, 116, 157, 162, 190] [2, 7, 31, 78, 93, 103, 158, 176, 193] [0, 8, 32, 79, 94, 104, 158, 165, 180] [1, 6, 30, 80, 95, 102, 160, 165, 193] [1, 16, 29, 81, 96, 112, 157, 161, 179] [2, 17, 27, 82, 97, 113, 161, 168, 183] [0, 15, 28, 83, 98, 111, 157, 163, 168] [10, 17, 25, 82, 84, 99, 160, 164, 182] [11, 15, 26, 83, 85, 100, 164, 171, 186] [9, 16, 24, 81, 86, 101, 160, 166, 171] [5, 19, 34, 87, 91, 102, 163, 167, 185] [3, 20, 35, 88, 92, 103, 167, 174, 189] [4, 18, 33, 89, 90, 104, 163, 169, 174] [4, 28, 32, 90, 100, 105, 166, 170, 188] [5, 29, 30, 91, 101, 106, 170, 177, 192] [3, 27, 31, 92, 99, 107, 166, 172, 177] [13, 20, 37, 93, 108, 109, 169, 173, 191] [14, 18, 38, 94, 109, 110, 156, 173, 180] [12, 19, 36, 95, 108, 110, 169, 175, 180] [7, 8, 22, 79, 96, 111, 172, 176, 194] [6, 8, 23, 80, 97, 112, 159, 176, 183] [6, 7, 21, 78, 98, 113, 172, 178, 183] [16, 31, 35, 88, 99, 114, 158, 175, 179] [17, 32, 33, 89, 100, 115, 162, 179, 186] [15, 30, 34, 87, 101, 116, 175, 181, 186] [40, 62, 64, 117, 136, 141, 156, 162, 165] [41, 60, 65, 118, 137, 142, 157, 175, 184] [39, 61, 63, 119, 135, 143, 158, 161, 173] [49, 50, 73, 120, 144, 145, 159, 165, 168] [48, 50, 74, 121, 145, 146, 160, 178, 187] [48, 49, 72, 122, 144, 146, 161, 164, 176] [43, 58, 77, 123, 147, 154, 162, 168, 171] [44, 59, 75, 124, 148, 155, 163, 181, 190] [42, 57, 76, 125, 149, 153, 164, 167, 179] [52, 65, 67, 124, 126, 150, 165, 171, 174] [53, 63, 68, 125, 127, 151, 166, 184, 193] [51, 64, 66, 123, 128, 152, 167, 170, 182] [53, 61, 76, 129, 133, 153, 168, 174, 177] [51, 62, 77, 130, 134, 154, 157, 169, 187] [52, 60, 75, 131, 132, 155, 170, 173, 185] [41, 46, 70, 117, 132, 142, 171, 177, 180] [39, 47, 71, 118, 133, 143, 160, 172, 190] [40, 45, 69, 119, 134, 141, 173, 176, 188] [40, 55, 68, 120, 135, 151, 174, 180, 183] [41, 56, 66, 121, 136, 152, 163, 175, 193] [39, 54, 67, 122, 137, 150, 176, 179, 191] [49, 56, 64, 121, 123, 138, 177, 183, 186] [50, 54, 65, 122, 124, 139, 157, 166, 178] [48, 55, 63, 120, 125, 140, 179, 182, 194] [44, 58, 73, 126, 130, 141, 180, 186, 189] [42, 59, 74, 127, 131, 142, 160, 169, 181] [43, 57, 72, 128, 129, 143, 158, 182, 185] [43, 67, 71, 129, 139, 144, 183, 189, 192] [44, 68, 69, 130, 140, 145, 163, 172, 184] [42, 66, 70, 131, 138, 146, 161, 185, 188] [52, 59, 76, 132, 147, 148, 156, 186, 192] [53, 57, 77, 133, 148, 149, 166, 175, 187] [51, 58, 75, 134, 147, 149, 164, 188, 191] [46, 47, 61, 118, 135, 150, 156, 159, 189] [45, 47, 62, 119, 136, 151, 169, 178, 190] [45, 46, 60, 117, 137, 152, 167, 191, 194] [55, 70, 74, 127, 138, 153, 159, 162, 192] [56, 71, 72, 128, 139, 154, 172, 181, 193] [54, 69, 73, 126, 140, 155, 158, 170, 194]
H_Z (78 checks, sparse supports)
[7, 8, 31, 39, 69, 72, 158, 172, 176] [14, 18, 20, 40, 52, 61, 156, 173, 174] [15, 16, 36, 41, 65, 77, 157, 171, 175] [10, 11, 34, 42, 72, 75, 164, 181, 185] [17, 21, 23, 43, 55, 64, 162, 182, 183] [0, 18, 19, 41, 44, 68, 163, 180, 184] [13, 14, 37, 39, 45, 75, 173, 190, 191] [20, 24, 26, 46, 58, 67, 171, 189, 191] [3, 21, 22, 44, 47, 71, 172, 189, 190] [1, 16, 17, 39, 42, 48, 160, 161, 179] [23, 27, 29, 49, 61, 70, 159, 161, 177] [6, 24, 25, 47, 50, 74, 159, 160, 178] [4, 19, 20, 42, 45, 51, 167, 169, 188] [26, 30, 32, 52, 64, 73, 165, 170, 186] [9, 27, 28, 50, 53, 77, 166, 168, 187] [7, 22, 23, 45, 48, 54, 176, 178, 194] [29, 33, 35, 55, 67, 76, 174, 179, 192] [12, 30, 31, 41, 53, 56, 175, 177, 193] [10, 25, 26, 48, 51, 57, 164, 182, 187] [32, 36, 38, 40, 58, 70, 162, 180, 188] [15, 33, 34, 44, 56, 59, 163, 181, 186] [13, 28, 29, 51, 54, 60, 157, 170, 191] [0, 2, 35, 43, 61, 73, 158, 168, 189] [18, 36, 37, 47, 59, 62, 156, 169, 190] [16, 31, 32, 54, 57, 63, 158, 166, 179] [3, 5, 38, 46, 64, 76, 156, 167, 177] [0, 1, 21, 50, 62, 65, 157, 165, 178] [19, 34, 35, 57, 60, 66, 167, 175, 185] [2, 6, 8, 40, 49, 67, 165, 176, 183] [3, 4, 24, 53, 65, 68, 166, 174, 184] [22, 37, 38, 60, 63, 69, 173, 184, 194] [5, 9, 11, 43, 52, 70, 171, 185, 192] [6, 7, 27, 56, 68, 71, 172, 183, 193] [1, 2, 25, 63, 66, 72, 161, 182, 193] [8, 12, 14, 46, 55, 73, 159, 180, 194] [9, 10, 30, 59, 71, 74, 160, 181, 192] [4, 5, 28, 66, 69, 75, 163, 170, 188] [11, 15, 17, 49, 58, 76, 164, 168, 186] [12, 13, 33, 62, 74, 77, 162, 169, 187] [85, 86, 109, 117, 147, 150, 156, 171, 191] [92, 96, 98, 118, 130, 139, 157, 172, 189] [93, 94, 114, 119, 143, 155, 158, 173, 190] [88, 89, 112, 120, 150, 153, 159, 174, 179] [95, 99, 101, 121, 133, 142, 160, 175, 177] [78, 96, 97, 119, 122, 146, 161, 176, 178] [91, 92, 115, 117, 123, 153, 162, 167, 177] [98, 102, 104, 124, 136, 145, 163, 165, 178] [81, 99, 100, 122, 125, 149, 164, 166, 179] [79, 94, 95, 117, 120, 126, 165, 180, 194] [101, 105, 107, 127, 139, 148, 166, 181, 192] [84, 102, 103, 125, 128, 152, 167, 182, 193] [82, 97, 98, 120, 123, 129, 168, 182, 183] [104, 108, 110, 130, 142, 151, 169, 180, 184] [87, 105, 106, 128, 131, 155, 170, 181, 185] [85, 100, 101, 123, 126, 132, 170, 171, 186] [107, 111, 113, 133, 145, 154, 168, 172, 187] [90, 108, 109, 119, 131, 134, 169, 173, 188] [88, 103, 104, 126, 129, 135, 158, 174, 189] [110, 114, 116, 118, 136, 148, 156, 175, 190] [93, 111, 112, 122, 134, 137, 157, 176, 191] [91, 106, 107, 129, 132, 138, 177, 185, 192] [78, 80, 113, 121, 139, 151, 178, 183, 193] [96, 114, 115, 125, 137, 140, 179, 184, 194] [94, 109, 110, 132, 135, 141, 156, 173, 180] [81, 83, 116, 124, 142, 154, 157, 171, 181] [78, 79, 99, 128, 140, 143, 158, 172, 182] [97, 112, 113, 135, 138, 144, 159, 161, 183] [80, 84, 86, 118, 127, 145, 159, 160, 184] [81, 82, 102, 131, 143, 146, 160, 161, 185] [100, 115, 116, 138, 141, 147, 162, 186, 188] [83, 87, 89, 121, 130, 148, 163, 186, 187] [84, 85, 105, 134, 146, 149, 164, 187, 188] [79, 80, 103, 141, 144, 150, 165, 176, 189] [86, 90, 92, 124, 133, 151, 166, 174, 190] [87, 88, 108, 137, 149, 152, 167, 175, 191] [82, 83, 106, 144, 147, 153, 164, 168, 192] [89, 93, 95, 127, 136, 154, 162, 169, 193] [90, 91, 111, 140, 152, 155, 163, 170, 194]
raw submission JSON