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[[87,22,3]] d =
n
87
k
22
d
3
kd²/n
2.276
w
11

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Distance

d_X 3 · witness weight 3 (claimed upper_bound)
witness operator (support, 3 qubits)
[45, 46, 49]
d_Z 3 · witness weight 3 (claimed upper_bound)
witness operator (support, 3 qubits)
[33, 48, 63]
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 sham5
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 20 · Z-checks 45
H_X (20 checks, sparse supports)
[0, 10, 20, 30, 40, 50, 60, 70, 75, 76] [1, 11, 21, 31, 41, 51, 61, 71, 77] [2, 12, 22, 32, 42, 52, 62, 72, 75, 77] [3, 13, 23, 33, 43, 53, 63, 73, 76, 77] [4, 14, 24, 34, 44, 54, 64, 74, 75, 76, 77] [5, 10, 25, 30, 45, 50, 65, 70, 78, 79] [6, 11, 26, 31, 46, 51, 66, 71, 80] [7, 12, 27, 32, 47, 52, 67, 72, 78, 80] [8, 13, 28, 33, 48, 53, 68, 73, 79, 80] [9, 14, 29, 34, 49, 54, 69, 74, 78, 79, 80] [15, 20, 25, 30, 55, 60, 65, 70, 81, 82] [16, 21, 26, 31, 56, 61, 66, 71, 83] [17, 22, 27, 32, 57, 62, 67, 72, 81, 83] [18, 23, 28, 33, 58, 63, 68, 73, 82, 83] [19, 24, 29, 34, 59, 64, 69, 74, 81, 82, 83] [35, 40, 45, 50, 55, 60, 65, 70, 84, 85] [36, 41, 46, 51, 56, 61, 66, 71, 86] [37, 42, 47, 52, 57, 62, 67, 72, 84, 86] [38, 43, 48, 53, 58, 63, 68, 73, 85, 86] [39, 44, 49, 54, 59, 64, 69, 74, 84, 85, 86]
H_Z (45 checks, sparse supports)
[0, 2, 4, 75] [0, 3, 4, 76] [1, 2, 3, 4, 77] [5, 7, 9, 78] [5, 8, 9, 79] [6, 7, 8, 9, 80] [10, 12, 14, 75, 78] [10, 13, 14, 76, 79] [11, 12, 13, 14, 77, 80] [15, 17, 19, 81] [15, 18, 19, 82] [16, 17, 18, 19, 83] [20, 22, 24, 75, 81] [20, 23, 24, 76, 82] [21, 22, 23, 24, 77, 83] [25, 27, 29, 78, 81] [25, 28, 29, 79, 82] [26, 27, 28, 29, 80, 83] [30, 32, 34, 75, 78, 81] [30, 33, 34, 76, 79, 82] [31, 32, 33, 34, 77, 80, 83] [35, 37, 39, 84] [35, 38, 39, 85] [36, 37, 38, 39, 86] [40, 42, 44, 75, 84] [40, 43, 44, 76, 85] [41, 42, 43, 44, 77, 86] [45, 47, 49, 78, 84] [45, 48, 49, 79, 85] [46, 47, 48, 49, 80, 86] [50, 52, 54, 75, 78, 84] [50, 53, 54, 76, 79, 85] [51, 52, 53, 54, 77, 80, 86] [55, 57, 59, 81, 84] [55, 58, 59, 82, 85] [56, 57, 58, 59, 83, 86] [60, 62, 64, 75, 81, 84] [60, 63, 64, 76, 82, 85] [61, 62, 63, 64, 77, 83, 86] [65, 67, 69, 78, 81, 84] [65, 68, 69, 79, 82, 85] [66, 67, 68, 69, 80, 83, 86] [70, 72, 74, 75, 78, 81, 84] [70, 73, 74, 76, 79, 82, 85] [71, 72, 73, 74, 77, 80, 83, 86]
raw submission JSON