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[[120,24,8]] d ≤
n
120
k
24
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)
[3, 9, 12, 26, 32, 35, 43, 44]
d_Z 8 · witness weight 8 (claimed upper_bound)
witness operator (support, 8 qubits)
[2, 13, 52, 57, 59, 61, 68, 70]
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(C3:C8,r=2) (order 24): a0=[5, 6, 15], a1=[0, 3, 4], b0=[1, 7, 13], b1=[0, 17, 22] 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 48 · Z-checks 48
H_X (48 checks, sparse supports)
[2, 3, 9, 48, 52, 53, 97, 103, 109] [3, 4, 10, 49, 53, 54, 96, 98, 118] [4, 5, 11, 50, 54, 55, 97, 99, 111] [5, 6, 12, 48, 51, 55, 98, 100, 112] [6, 7, 13, 48, 49, 52, 99, 101, 105] [0, 7, 14, 49, 50, 53, 100, 102, 114] [0, 1, 15, 50, 51, 54, 101, 103, 107] [1, 2, 8, 51, 52, 55, 96, 102, 116] [1, 10, 19, 56, 60, 69, 105, 111, 117] [2, 11, 20, 57, 61, 70, 102, 104, 106] [3, 12, 21, 58, 62, 71, 105, 107, 119] [4, 13, 22, 59, 63, 64, 96, 106, 108] [5, 14, 23, 56, 60, 65, 107, 109, 113] [6, 15, 16, 57, 61, 66, 98, 108, 110] [7, 8, 17, 58, 62, 67, 109, 111, 115] [0, 9, 18, 59, 63, 68, 100, 104, 110] [11, 17, 18, 61, 64, 68, 101, 113, 119] [12, 18, 19, 62, 65, 69, 110, 112, 114] [13, 19, 20, 63, 66, 70, 103, 113, 115] [14, 20, 21, 56, 67, 71, 104, 114, 116] [15, 21, 22, 57, 64, 68, 97, 115, 117] [8, 22, 23, 58, 65, 69, 106, 116, 118] [9, 16, 23, 59, 66, 70, 99, 117, 119] [10, 16, 17, 60, 67, 71, 108, 112, 118] [26, 27, 33, 72, 76, 77, 96, 113, 118] [27, 28, 34, 73, 77, 78, 97, 106, 111] [28, 29, 35, 74, 78, 79, 98, 112, 115] [29, 30, 36, 72, 75, 79, 99, 105, 108] [30, 31, 37, 72, 73, 76, 100, 114, 117] [24, 31, 38, 73, 74, 77, 101, 107, 110] [24, 25, 39, 74, 75, 78, 102, 116, 119] [25, 26, 32, 75, 76, 79, 103, 104, 109] [25, 34, 43, 80, 84, 93, 97, 102, 104] [26, 35, 44, 81, 85, 94, 105, 114, 119] [27, 36, 45, 82, 86, 95, 96, 99, 106] [28, 37, 46, 83, 87, 88, 107, 113, 116] [29, 38, 47, 80, 84, 89, 98, 101, 108] [30, 39, 40, 81, 85, 90, 109, 115, 118] [31, 32, 41, 82, 86, 91, 100, 103, 110] [24, 33, 42, 83, 87, 92, 111, 112, 117] [35, 41, 42, 85, 88, 92, 105, 110, 112] [36, 42, 43, 86, 89, 93, 98, 103, 113] [37, 43, 44, 87, 90, 94, 104, 107, 114] [38, 44, 45, 80, 91, 95, 97, 100, 115] [39, 45, 46, 81, 88, 92, 106, 109, 116] [32, 46, 47, 82, 89, 93, 99, 102, 117] [33, 40, 47, 83, 90, 94, 108, 111, 118] [34, 40, 41, 84, 91, 95, 96, 101, 119]
H_Z (48 checks, sparse supports)
[1, 7, 11, 24, 34, 47, 101, 102, 111] [0, 2, 20, 25, 32, 43, 102, 103, 104] [1, 3, 13, 26, 36, 41, 96, 103, 105] [2, 4, 22, 27, 34, 45, 96, 97, 106] [3, 5, 15, 28, 38, 43, 97, 98, 107] [4, 6, 16, 29, 36, 47, 98, 99, 108] [5, 7, 9, 30, 32, 45, 99, 100, 109] [0, 6, 18, 31, 38, 41, 100, 101, 110] [9, 15, 19, 31, 32, 42, 103, 110, 117] [4, 8, 10, 27, 33, 40, 96, 111, 118] [9, 11, 21, 25, 34, 44, 97, 104, 119] [6, 10, 12, 29, 35, 42, 98, 105, 112] [11, 13, 23, 27, 36, 46, 99, 106, 113] [0, 12, 14, 31, 37, 44, 100, 107, 114] [13, 15, 17, 29, 38, 40, 101, 108, 115] [2, 8, 14, 25, 39, 46, 102, 109, 116] [3, 17, 23, 26, 39, 40, 109, 118, 119] [12, 16, 18, 24, 35, 41, 110, 112, 119] [5, 17, 19, 28, 33, 42, 111, 112, 113] [14, 18, 20, 26, 37, 43, 104, 113, 114] [7, 19, 21, 30, 35, 44, 105, 114, 115] [8, 20, 22, 28, 39, 45, 106, 115, 116] [1, 21, 23, 24, 37, 46, 107, 116, 117] [10, 16, 22, 30, 33, 47, 108, 117, 118] [49, 55, 59, 72, 82, 95, 96, 99, 100] [48, 50, 68, 73, 80, 91, 97, 100, 101] [49, 51, 61, 74, 84, 89, 98, 101, 102] [50, 52, 70, 75, 82, 93, 99, 102, 103] [51, 53, 63, 76, 86, 91, 96, 100, 103] [52, 54, 64, 77, 84, 95, 96, 97, 101] [53, 55, 57, 78, 80, 93, 97, 98, 102] [48, 54, 66, 79, 86, 89, 98, 99, 103] [57, 63, 67, 79, 80, 90, 104, 108, 115] [52, 56, 58, 75, 81, 88, 105, 109, 116] [57, 59, 69, 73, 82, 92, 106, 110, 117] [54, 58, 60, 77, 83, 90, 107, 111, 118] [59, 61, 71, 75, 84, 94, 104, 108, 119] [48, 60, 62, 79, 85, 92, 105, 109, 112] [61, 63, 65, 77, 86, 88, 106, 110, 113] [50, 56, 62, 73, 87, 94, 107, 111, 114] [51, 65, 71, 74, 87, 88, 107, 112, 116] [60, 64, 66, 72, 83, 89, 108, 113, 117] [53, 65, 67, 76, 81, 90, 109, 114, 118] [62, 66, 68, 74, 85, 91, 110, 115, 119] [55, 67, 69, 78, 83, 92, 111, 112, 116] [56, 68, 70, 76, 87, 93, 104, 113, 117] [49, 69, 71, 72, 85, 94, 105, 114, 118] [58, 64, 70, 78, 81, 95, 106, 115, 119]
raw submission JSON