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[[241,121,3]] d ≤
n
241
k
121
d
3
kd²/n
4.519
w
12

Share this result

Distance

d_X 3 · witness weight 3 (claimed upper_bound)
witness operator (support, 3 qubits)
[46, 56, 58]
d_Z 3 · witness weight 3 (claimed upper_bound)
witness operator (support, 3 qubits)
[8, 53, 68]
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 ham15 and ham15
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 60 · Z-checks 60
H_X (60 checks, sparse supports)
[0, 30, 60, 90, 120, 150, 180, 210, 225] [1, 31, 61, 91, 121, 151, 181, 211, 226] [2, 32, 62, 92, 122, 152, 182, 212, 225, 226] [3, 33, 63, 93, 123, 153, 183, 213, 227] [4, 34, 64, 94, 124, 154, 184, 214, 225, 227] [5, 35, 65, 95, 125, 155, 185, 215, 226, 227] [6, 36, 66, 96, 126, 156, 186, 216, 225, 226, 227] [7, 37, 67, 97, 127, 157, 187, 217, 228] [8, 38, 68, 98, 128, 158, 188, 218, 225, 228] [9, 39, 69, 99, 129, 159, 189, 219, 226, 228] [10, 40, 70, 100, 130, 160, 190, 220, 225, 226, 228] [11, 41, 71, 101, 131, 161, 191, 221, 227, 228] [12, 42, 72, 102, 132, 162, 192, 222, 225, 227, 228] [13, 43, 73, 103, 133, 163, 193, 223, 226, 227, 228] [14, 44, 74, 104, 134, 164, 194, 224, 225, 226, 227, 228] [15, 30, 75, 90, 135, 150, 195, 210, 229] [16, 31, 76, 91, 136, 151, 196, 211, 230] [17, 32, 77, 92, 137, 152, 197, 212, 229, 230] [18, 33, 78, 93, 138, 153, 198, 213, 231] [19, 34, 79, 94, 139, 154, 199, 214, 229, 231] [20, 35, 80, 95, 140, 155, 200, 215, 230, 231] [21, 36, 81, 96, 141, 156, 201, 216, 229, 230, 231] [22, 37, 82, 97, 142, 157, 202, 217, 232] [23, 38, 83, 98, 143, 158, 203, 218, 229, 232] [24, 39, 84, 99, 144, 159, 204, 219, 230, 232] [25, 40, 85, 100, 145, 160, 205, 220, 229, 230, 232] [26, 41, 86, 101, 146, 161, 206, 221, 231, 232] [27, 42, 87, 102, 147, 162, 207, 222, 229, 231, 232] [28, 43, 88, 103, 148, 163, 208, 223, 230, 231, 232] [29, 44, 89, 104, 149, 164, 209, 224, 229, 230, 231, 232] [45, 60, 75, 90, 165, 180, 195, 210, 233] [46, 61, 76, 91, 166, 181, 196, 211, 234] [47, 62, 77, 92, 167, 182, 197, 212, 233, 234] [48, 63, 78, 93, 168, 183, 198, 213, 235] [49, 64, 79, 94, 169, 184, 199, 214, 233, 235] [50, 65, 80, 95, 170, 185, 200, 215, 234, 235] [51, 66, 81, 96, 171, 186, 201, 216, 233, 234, 235] [52, 67, 82, 97, 172, 187, 202, 217, 236] [53, 68, 83, 98, 173, 188, 203, 218, 233, 236] [54, 69, 84, 99, 174, 189, 204, 219, 234, 236] [55, 70, 85, 100, 175, 190, 205, 220, 233, 234, 236] [56, 71, 86, 101, 176, 191, 206, 221, 235, 236] [57, 72, 87, 102, 177, 192, 207, 222, 233, 235, 236] [58, 73, 88, 103, 178, 193, 208, 223, 234, 235, 236] [59, 74, 89, 104, 179, 194, 209, 224, 233, 234, 235, 236] [105, 120, 135, 150, 165, 180, 195, 210, 237] [106, 121, 136, 151, 166, 181, 196, 211, 238] [107, 122, 137, 152, 167, 182, 197, 212, 237, 238] [108, 123, 138, 153, 168, 183, 198, 213, 239] [109, 124, 139, 154, 169, 184, 199, 214, 237, 239] [110, 125, 140, 155, 170, 185, 200, 215, 238, 239] [111, 126, 141, 156, 171, 186, 201, 216, 237, 238, 239] [112, 127, 142, 157, 172, 187, 202, 217, 240] [113, 128, 143, 158, 173, 188, 203, 218, 237, 240] [114, 129, 144, 159, 174, 189, 204, 219, 238, 240] [115, 130, 145, 160, 175, 190, 205, 220, 237, 238, 240] [116, 131, 146, 161, 176, 191, 206, 221, 239, 240] [117, 132, 147, 162, 177, 192, 207, 222, 237, 239, 240] [118, 133, 148, 163, 178, 193, 208, 223, 238, 239, 240] [119, 134, 149, 164, 179, 194, 209, 224, 237, 238, 239, 240]
H_Z (60 checks, sparse supports)
[0, 2, 4, 6, 8, 10, 12, 14, 225] [1, 2, 5, 6, 9, 10, 13, 14, 226] [3, 4, 5, 6, 11, 12, 13, 14, 227] [7, 8, 9, 10, 11, 12, 13, 14, 228] [15, 17, 19, 21, 23, 25, 27, 29, 229] [16, 17, 20, 21, 24, 25, 28, 29, 230] [18, 19, 20, 21, 26, 27, 28, 29, 231] [22, 23, 24, 25, 26, 27, 28, 29, 232] [30, 32, 34, 36, 38, 40, 42, 44, 225, 229] [31, 32, 35, 36, 39, 40, 43, 44, 226, 230] [33, 34, 35, 36, 41, 42, 43, 44, 227, 231] [37, 38, 39, 40, 41, 42, 43, 44, 228, 232] [45, 47, 49, 51, 53, 55, 57, 59, 233] [46, 47, 50, 51, 54, 55, 58, 59, 234] [48, 49, 50, 51, 56, 57, 58, 59, 235] [52, 53, 54, 55, 56, 57, 58, 59, 236] [60, 62, 64, 66, 68, 70, 72, 74, 225, 233] [61, 62, 65, 66, 69, 70, 73, 74, 226, 234] [63, 64, 65, 66, 71, 72, 73, 74, 227, 235] [67, 68, 69, 70, 71, 72, 73, 74, 228, 236] [75, 77, 79, 81, 83, 85, 87, 89, 229, 233] [76, 77, 80, 81, 84, 85, 88, 89, 230, 234] [78, 79, 80, 81, 86, 87, 88, 89, 231, 235] [82, 83, 84, 85, 86, 87, 88, 89, 232, 236] [90, 92, 94, 96, 98, 100, 102, 104, 225, 229, 233] [91, 92, 95, 96, 99, 100, 103, 104, 226, 230, 234] [93, 94, 95, 96, 101, 102, 103, 104, 227, 231, 235] [97, 98, 99, 100, 101, 102, 103, 104, 228, 232, 236] [105, 107, 109, 111, 113, 115, 117, 119, 237] [106, 107, 110, 111, 114, 115, 118, 119, 238] [108, 109, 110, 111, 116, 117, 118, 119, 239] [112, 113, 114, 115, 116, 117, 118, 119, 240] [120, 122, 124, 126, 128, 130, 132, 134, 225, 237] [121, 122, 125, 126, 129, 130, 133, 134, 226, 238] [123, 124, 125, 126, 131, 132, 133, 134, 227, 239] [127, 128, 129, 130, 131, 132, 133, 134, 228, 240] [135, 137, 139, 141, 143, 145, 147, 149, 229, 237] [136, 137, 140, 141, 144, 145, 148, 149, 230, 238] [138, 139, 140, 141, 146, 147, 148, 149, 231, 239] [142, 143, 144, 145, 146, 147, 148, 149, 232, 240] [150, 152, 154, 156, 158, 160, 162, 164, 225, 229, 237] [151, 152, 155, 156, 159, 160, 163, 164, 226, 230, 238] [153, 154, 155, 156, 161, 162, 163, 164, 227, 231, 239] [157, 158, 159, 160, 161, 162, 163, 164, 228, 232, 240] [165, 167, 169, 171, 173, 175, 177, 179, 233, 237] [166, 167, 170, 171, 174, 175, 178, 179, 234, 238] [168, 169, 170, 171, 176, 177, 178, 179, 235, 239] [172, 173, 174, 175, 176, 177, 178, 179, 236, 240] [180, 182, 184, 186, 188, 190, 192, 194, 225, 233, 237] [181, 182, 185, 186, 189, 190, 193, 194, 226, 234, 238] [183, 184, 185, 186, 191, 192, 193, 194, 227, 235, 239] [187, 188, 189, 190, 191, 192, 193, 194, 228, 236, 240] [195, 197, 199, 201, 203, 205, 207, 209, 229, 233, 237] [196, 197, 200, 201, 204, 205, 208, 209, 230, 234, 238] [198, 199, 200, 201, 206, 207, 208, 209, 231, 235, 239] [202, 203, 204, 205, 206, 207, 208, 209, 232, 236, 240] [210, 212, 214, 216, 218, 220, 222, 224, 225, 229, 233, 237] [211, 212, 215, 216, 219, 220, 223, 224, 226, 230, 234, 238] [213, 214, 215, 216, 221, 222, 223, 224, 227, 231, 235, 239] [217, 218, 219, 220, 221, 222, 223, 224, 228, 232, 236, 240]
raw submission JSON