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[[232,104,3]] d ≤
n
232
k
104
d
3
kd²/n
4.034
w
19

Share this result

Distance

d_X 3 · witness weight 3 (claimed upper_bound)
witness operator (support, 3 qubits)
[29, 31, 33]
d_Z 3 · witness weight 3 (claimed upper_bound)
witness operator (support, 3 qubits)
[8, 190, 204]
certificate none yet · distance stands as a self-certified upper bound (d ≤)

Construction & provenance

authors @mathysrennela
provenance submitted through the challenge
novelty novelty not audited
construction Hypergraph product of classical codes ham31 and ham7
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 35 · Z-checks 93
H_X (35 checks, sparse supports)
[0, 14, 28, 42, 56, 70, 84, 98, 112, 126, 140, 154, 168, 182, 196, 210, 217] [1, 15, 29, 43, 57, 71, 85, 99, 113, 127, 141, 155, 169, 183, 197, 211, 218] [2, 16, 30, 44, 58, 72, 86, 100, 114, 128, 142, 156, 170, 184, 198, 212, 217, 218] [3, 17, 31, 45, 59, 73, 87, 101, 115, 129, 143, 157, 171, 185, 199, 213, 219] [4, 18, 32, 46, 60, 74, 88, 102, 116, 130, 144, 158, 172, 186, 200, 214, 217, 219] [5, 19, 33, 47, 61, 75, 89, 103, 117, 131, 145, 159, 173, 187, 201, 215, 218, 219] [6, 20, 34, 48, 62, 76, 90, 104, 118, 132, 146, 160, 174, 188, 202, 216, 217, 218, 219] [7, 14, 35, 42, 63, 70, 91, 98, 119, 126, 147, 154, 175, 182, 203, 210, 220] [8, 15, 36, 43, 64, 71, 92, 99, 120, 127, 148, 155, 176, 183, 204, 211, 221] [9, 16, 37, 44, 65, 72, 93, 100, 121, 128, 149, 156, 177, 184, 205, 212, 220, 221] [10, 17, 38, 45, 66, 73, 94, 101, 122, 129, 150, 157, 178, 185, 206, 213, 222] [11, 18, 39, 46, 67, 74, 95, 102, 123, 130, 151, 158, 179, 186, 207, 214, 220, 222] [12, 19, 40, 47, 68, 75, 96, 103, 124, 131, 152, 159, 180, 187, 208, 215, 221, 222] [13, 20, 41, 48, 69, 76, 97, 104, 125, 132, 153, 160, 181, 188, 209, 216, 220, 221, 222] [21, 28, 35, 42, 77, 84, 91, 98, 133, 140, 147, 154, 189, 196, 203, 210, 223] [22, 29, 36, 43, 78, 85, 92, 99, 134, 141, 148, 155, 190, 197, 204, 211, 224] [23, 30, 37, 44, 79, 86, 93, 100, 135, 142, 149, 156, 191, 198, 205, 212, 223, 224] [24, 31, 38, 45, 80, 87, 94, 101, 136, 143, 150, 157, 192, 199, 206, 213, 225] [25, 32, 39, 46, 81, 88, 95, 102, 137, 144, 151, 158, 193, 200, 207, 214, 223, 225] [26, 33, 40, 47, 82, 89, 96, 103, 138, 145, 152, 159, 194, 201, 208, 215, 224, 225] [27, 34, 41, 48, 83, 90, 97, 104, 139, 146, 153, 160, 195, 202, 209, 216, 223, 224, 225] [49, 56, 63, 70, 77, 84, 91, 98, 161, 168, 175, 182, 189, 196, 203, 210, 226] [50, 57, 64, 71, 78, 85, 92, 99, 162, 169, 176, 183, 190, 197, 204, 211, 227] [51, 58, 65, 72, 79, 86, 93, 100, 163, 170, 177, 184, 191, 198, 205, 212, 226, 227] [52, 59, 66, 73, 80, 87, 94, 101, 164, 171, 178, 185, 192, 199, 206, 213, 228] [53, 60, 67, 74, 81, 88, 95, 102, 165, 172, 179, 186, 193, 200, 207, 214, 226, 228] [54, 61, 68, 75, 82, 89, 96, 103, 166, 173, 180, 187, 194, 201, 208, 215, 227, 228] [55, 62, 69, 76, 83, 90, 97, 104, 167, 174, 181, 188, 195, 202, 209, 216, 226, 227, 228] [105, 112, 119, 126, 133, 140, 147, 154, 161, 168, 175, 182, 189, 196, 203, 210, 229] [106, 113, 120, 127, 134, 141, 148, 155, 162, 169, 176, 183, 190, 197, 204, 211, 230] [107, 114, 121, 128, 135, 142, 149, 156, 163, 170, 177, 184, 191, 198, 205, 212, 229, 230] [108, 115, 122, 129, 136, 143, 150, 157, 164, 171, 178, 185, 192, 199, 206, 213, 231] [109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 200, 207, 214, 229, 231] [110, 117, 124, 131, 138, 145, 152, 159, 166, 173, 180, 187, 194, 201, 208, 215, 230, 231] [111, 118, 125, 132, 139, 146, 153, 160, 167, 174, 181, 188, 195, 202, 209, 216, 229, 230, 231]
H_Z (93 checks, sparse supports)
[0, 2, 4, 6, 217] [1, 2, 5, 6, 218] [3, 4, 5, 6, 219] [7, 9, 11, 13, 220] [8, 9, 12, 13, 221] [10, 11, 12, 13, 222] [14, 16, 18, 20, 217, 220] [15, 16, 19, 20, 218, 221] [17, 18, 19, 20, 219, 222] [21, 23, 25, 27, 223] [22, 23, 26, 27, 224] [24, 25, 26, 27, 225] [28, 30, 32, 34, 217, 223] [29, 30, 33, 34, 218, 224] [31, 32, 33, 34, 219, 225] [35, 37, 39, 41, 220, 223] [36, 37, 40, 41, 221, 224] [38, 39, 40, 41, 222, 225] [42, 44, 46, 48, 217, 220, 223] [43, 44, 47, 48, 218, 221, 224] [45, 46, 47, 48, 219, 222, 225] [49, 51, 53, 55, 226] [50, 51, 54, 55, 227] [52, 53, 54, 55, 228] [56, 58, 60, 62, 217, 226] [57, 58, 61, 62, 218, 227] [59, 60, 61, 62, 219, 228] [63, 65, 67, 69, 220, 226] [64, 65, 68, 69, 221, 227] [66, 67, 68, 69, 222, 228] [70, 72, 74, 76, 217, 220, 226] [71, 72, 75, 76, 218, 221, 227] [73, 74, 75, 76, 219, 222, 228] [77, 79, 81, 83, 223, 226] [78, 79, 82, 83, 224, 227] [80, 81, 82, 83, 225, 228] [84, 86, 88, 90, 217, 223, 226] [85, 86, 89, 90, 218, 224, 227] [87, 88, 89, 90, 219, 225, 228] [91, 93, 95, 97, 220, 223, 226] [92, 93, 96, 97, 221, 224, 227] [94, 95, 96, 97, 222, 225, 228] [98, 100, 102, 104, 217, 220, 223, 226] [99, 100, 103, 104, 218, 221, 224, 227] [101, 102, 103, 104, 219, 222, 225, 228] [105, 107, 109, 111, 229] [106, 107, 110, 111, 230] [108, 109, 110, 111, 231] [112, 114, 116, 118, 217, 229] [113, 114, 117, 118, 218, 230] [115, 116, 117, 118, 219, 231] [119, 121, 123, 125, 220, 229] [120, 121, 124, 125, 221, 230] [122, 123, 124, 125, 222, 231] [126, 128, 130, 132, 217, 220, 229] [127, 128, 131, 132, 218, 221, 230] [129, 130, 131, 132, 219, 222, 231] [133, 135, 137, 139, 223, 229] [134, 135, 138, 139, 224, 230] [136, 137, 138, 139, 225, 231] [140, 142, 144, 146, 217, 223, 229] [141, 142, 145, 146, 218, 224, 230] [143, 144, 145, 146, 219, 225, 231] [147, 149, 151, 153, 220, 223, 229] [148, 149, 152, 153, 221, 224, 230] [150, 151, 152, 153, 222, 225, 231] [154, 156, 158, 160, 217, 220, 223, 229] [155, 156, 159, 160, 218, 221, 224, 230] [157, 158, 159, 160, 219, 222, 225, 231] [161, 163, 165, 167, 226, 229] [162, 163, 166, 167, 227, 230] [164, 165, 166, 167, 228, 231] [168, 170, 172, 174, 217, 226, 229] [169, 170, 173, 174, 218, 227, 230] [171, 172, 173, 174, 219, 228, 231] [175, 177, 179, 181, 220, 226, 229] [176, 177, 180, 181, 221, 227, 230] [178, 179, 180, 181, 222, 228, 231] [182, 184, 186, 188, 217, 220, 226, 229] [183, 184, 187, 188, 218, 221, 227, 230] [185, 186, 187, 188, 219, 222, 228, 231] [189, 191, 193, 195, 223, 226, 229] [190, 191, 194, 195, 224, 227, 230] [192, 193, 194, 195, 225, 228, 231] [196, 198, 200, 202, 217, 223, 226, 229] [197, 198, 201, 202, 218, 224, 227, 230] [199, 200, 201, 202, 219, 225, 228, 231] [203, 205, 207, 209, 220, 223, 226, 229] [204, 205, 208, 209, 221, 224, 227, 230] [206, 207, 208, 209, 222, 225, 228, 231] [210, 212, 214, 216, 217, 220, 223, 226, 229] [211, 212, 215, 216, 218, 221, 224, 227, 230] [213, 214, 215, 216, 219, 222, 225, 228, 231]
raw submission JSON