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[[102,33,3]] d =
n
102
k
33
d
3
kd²/n
2.912
w
11

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Distance

d_X 3 · witness weight 3 (claimed upper_bound)
witness operator (support, 3 qubits)
[54, 56, 58]
d_Z 3 · witness weight 3 (claimed upper_bound)
witness operator (support, 3 qubits)
[41, 59, 77]
certificate exact, d = 3 · scipy/HiGHS MILP
X: no logical < 3 exists; Z: no logical < 3 exists

Construction & provenance

authors @mathysrennela
provenance submitted through the challenge
novelty novelty not audited
construction Hypergraph product of classical codes ham15 and sham6
model Tencent Hy3 (claimed, not verified)
builds on arXiv:0903.0566
date 2026-07-17
family hypergraph 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 24 · Z-checks 45
H_X (24 checks, sparse supports)
[0, 12, 24, 36, 48, 60, 72, 84, 91] [1, 13, 25, 37, 49, 61, 73, 85, 90, 91] [2, 14, 26, 38, 50, 62, 74, 86, 92] [3, 15, 27, 39, 51, 63, 75, 87, 90, 92] [4, 16, 28, 40, 52, 64, 76, 88, 91, 92] [5, 17, 29, 41, 53, 65, 77, 89, 90, 91, 92] [6, 12, 30, 36, 54, 60, 78, 84, 94] [7, 13, 31, 37, 55, 61, 79, 85, 93, 94] [8, 14, 32, 38, 56, 62, 80, 86, 95] [9, 15, 33, 39, 57, 63, 81, 87, 93, 95] [10, 16, 34, 40, 58, 64, 82, 88, 94, 95] [11, 17, 35, 41, 59, 65, 83, 89, 93, 94, 95] [18, 24, 30, 36, 66, 72, 78, 84, 97] [19, 25, 31, 37, 67, 73, 79, 85, 96, 97] [20, 26, 32, 38, 68, 74, 80, 86, 98] [21, 27, 33, 39, 69, 75, 81, 87, 96, 98] [22, 28, 34, 40, 70, 76, 82, 88, 97, 98] [23, 29, 35, 41, 71, 77, 83, 89, 96, 97, 98] [42, 48, 54, 60, 66, 72, 78, 84, 100] [43, 49, 55, 61, 67, 73, 79, 85, 99, 100] [44, 50, 56, 62, 68, 74, 80, 86, 101] [45, 51, 57, 63, 69, 75, 81, 87, 99, 101] [46, 52, 58, 64, 70, 76, 82, 88, 100, 101] [47, 53, 59, 65, 71, 77, 83, 89, 99, 100, 101]
H_Z (45 checks, sparse supports)
[1, 3, 5, 90] [0, 1, 4, 5, 91] [2, 3, 4, 5, 92] [7, 9, 11, 93] [6, 7, 10, 11, 94] [8, 9, 10, 11, 95] [13, 15, 17, 90, 93] [12, 13, 16, 17, 91, 94] [14, 15, 16, 17, 92, 95] [19, 21, 23, 96] [18, 19, 22, 23, 97] [20, 21, 22, 23, 98] [25, 27, 29, 90, 96] [24, 25, 28, 29, 91, 97] [26, 27, 28, 29, 92, 98] [31, 33, 35, 93, 96] [30, 31, 34, 35, 94, 97] [32, 33, 34, 35, 95, 98] [37, 39, 41, 90, 93, 96] [36, 37, 40, 41, 91, 94, 97] [38, 39, 40, 41, 92, 95, 98] [43, 45, 47, 99] [42, 43, 46, 47, 100] [44, 45, 46, 47, 101] [49, 51, 53, 90, 99] [48, 49, 52, 53, 91, 100] [50, 51, 52, 53, 92, 101] [55, 57, 59, 93, 99] [54, 55, 58, 59, 94, 100] [56, 57, 58, 59, 95, 101] [61, 63, 65, 90, 93, 99] [60, 61, 64, 65, 91, 94, 100] [62, 63, 64, 65, 92, 95, 101] [67, 69, 71, 96, 99] [66, 67, 70, 71, 97, 100] [68, 69, 70, 71, 98, 101] [73, 75, 77, 90, 96, 99] [72, 73, 76, 77, 91, 97, 100] [74, 75, 76, 77, 92, 98, 101] [79, 81, 83, 93, 96, 99] [78, 79, 82, 83, 94, 97, 100] [80, 81, 82, 83, 95, 98, 101] [85, 87, 89, 90, 93, 96, 99] [84, 85, 88, 89, 91, 94, 97, 100] [86, 87, 88, 89, 92, 95, 98, 101]
raw submission JSON