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[[281,121,4]] d ≤
n
281
k
121
d
4
kd²/n
6.89
w
21

Share this result

Distance

d_X 4 · witness weight 4 (claimed upper_bound)
witness operator (support, 4 qubits)
[49, 56, 58, 63]
d_Z 4 · witness weight 4 (claimed upper_bound)
witness operator (support, 4 qubits)
[127, 159, 207, 239]
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 eham16 and eham16
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 80 · Z-checks 80
H_X (80 checks, sparse supports)
[0, 32, 64, 96, 128, 160, 192, 224, 256, 260] [1, 33, 65, 97, 129, 161, 193, 225, 257, 260] [2, 34, 66, 98, 130, 162, 194, 226, 256, 257, 260] [3, 35, 67, 99, 131, 163, 195, 227, 258, 260] [4, 36, 68, 100, 132, 164, 196, 228, 256, 258, 260] [5, 37, 69, 101, 133, 165, 197, 229, 257, 258, 260] [6, 38, 70, 102, 134, 166, 198, 230, 256, 257, 258, 260] [7, 39, 71, 103, 135, 167, 199, 231, 259, 260] [8, 40, 72, 104, 136, 168, 200, 232, 256, 259, 260] [9, 41, 73, 105, 137, 169, 201, 233, 257, 259, 260] [10, 42, 74, 106, 138, 170, 202, 234, 256, 257, 259, 260] [11, 43, 75, 107, 139, 171, 203, 235, 258, 259, 260] [12, 44, 76, 108, 140, 172, 204, 236, 256, 258, 259, 260] [13, 45, 77, 109, 141, 173, 205, 237, 257, 258, 259, 260] [14, 46, 78, 110, 142, 174, 206, 238, 256, 257, 258, 259, 260] [15, 47, 79, 111, 143, 175, 207, 239, 260] [16, 32, 80, 96, 144, 160, 208, 224, 261, 265] [17, 33, 81, 97, 145, 161, 209, 225, 262, 265] [18, 34, 82, 98, 146, 162, 210, 226, 261, 262, 265] [19, 35, 83, 99, 147, 163, 211, 227, 263, 265] [20, 36, 84, 100, 148, 164, 212, 228, 261, 263, 265] [21, 37, 85, 101, 149, 165, 213, 229, 262, 263, 265] [22, 38, 86, 102, 150, 166, 214, 230, 261, 262, 263, 265] [23, 39, 87, 103, 151, 167, 215, 231, 264, 265] [24, 40, 88, 104, 152, 168, 216, 232, 261, 264, 265] [25, 41, 89, 105, 153, 169, 217, 233, 262, 264, 265] [26, 42, 90, 106, 154, 170, 218, 234, 261, 262, 264, 265] [27, 43, 91, 107, 155, 171, 219, 235, 263, 264, 265] [28, 44, 92, 108, 156, 172, 220, 236, 261, 263, 264, 265] [29, 45, 93, 109, 157, 173, 221, 237, 262, 263, 264, 265] [30, 46, 94, 110, 158, 174, 222, 238, 261, 262, 263, 264, 265] [31, 47, 95, 111, 159, 175, 223, 239, 265] [48, 64, 80, 96, 176, 192, 208, 224, 266, 270] [49, 65, 81, 97, 177, 193, 209, 225, 267, 270] [50, 66, 82, 98, 178, 194, 210, 226, 266, 267, 270] [51, 67, 83, 99, 179, 195, 211, 227, 268, 270] [52, 68, 84, 100, 180, 196, 212, 228, 266, 268, 270] [53, 69, 85, 101, 181, 197, 213, 229, 267, 268, 270] [54, 70, 86, 102, 182, 198, 214, 230, 266, 267, 268, 270] [55, 71, 87, 103, 183, 199, 215, 231, 269, 270] [56, 72, 88, 104, 184, 200, 216, 232, 266, 269, 270] [57, 73, 89, 105, 185, 201, 217, 233, 267, 269, 270] [58, 74, 90, 106, 186, 202, 218, 234, 266, 267, 269, 270] [59, 75, 91, 107, 187, 203, 219, 235, 268, 269, 270] [60, 76, 92, 108, 188, 204, 220, 236, 266, 268, 269, 270] [61, 77, 93, 109, 189, 205, 221, 237, 267, 268, 269, 270] [62, 78, 94, 110, 190, 206, 222, 238, 266, 267, 268, 269, 270] [63, 79, 95, 111, 191, 207, 223, 239, 270] [112, 128, 144, 160, 176, 192, 208, 224, 271, 275] [113, 129, 145, 161, 177, 193, 209, 225, 272, 275] [114, 130, 146, 162, 178, 194, 210, 226, 271, 272, 275] [115, 131, 147, 163, 179, 195, 211, 227, 273, 275] [116, 132, 148, 164, 180, 196, 212, 228, 271, 273, 275] [117, 133, 149, 165, 181, 197, 213, 229, 272, 273, 275] [118, 134, 150, 166, 182, 198, 214, 230, 271, 272, 273, 275] [119, 135, 151, 167, 183, 199, 215, 231, 274, 275] [120, 136, 152, 168, 184, 200, 216, 232, 271, 274, 275] [121, 137, 153, 169, 185, 201, 217, 233, 272, 274, 275] [122, 138, 154, 170, 186, 202, 218, 234, 271, 272, 274, 275] [123, 139, 155, 171, 187, 203, 219, 235, 273, 274, 275] [124, 140, 156, 172, 188, 204, 220, 236, 271, 273, 274, 275] [125, 141, 157, 173, 189, 205, 221, 237, 272, 273, 274, 275] [126, 142, 158, 174, 190, 206, 222, 238, 271, 272, 273, 274, 275] [127, 143, 159, 175, 191, 207, 223, 239, 275] [0, 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, 176, 192, 208, 224, 240, 276, 280] [1, 17, 33, 49, 65, 81, 97, 113, 129, 145, 161, 177, 193, 209, 225, 241, 277, 280] [2, 18, 34, 50, 66, 82, 98, 114, 130, 146, 162, 178, 194, 210, 226, 242, 276, 277, 280] [3, 19, 35, 51, 67, 83, 99, 115, 131, 147, 163, 179, 195, 211, 227, 243, 278, 280] [4, 20, 36, 52, 68, 84, 100, 116, 132, 148, 164, 180, 196, 212, 228, 244, 276, 278, 280] [5, 21, 37, 53, 69, 85, 101, 117, 133, 149, 165, 181, 197, 213, 229, 245, 277, 278, 280] [6, 22, 38, 54, 70, 86, 102, 118, 134, 150, 166, 182, 198, 214, 230, 246, 276, 277, 278, 280] [7, 23, 39, 55, 71, 87, 103, 119, 135, 151, 167, 183, 199, 215, 231, 247, 279, 280] [8, 24, 40, 56, 72, 88, 104, 120, 136, 152, 168, 184, 200, 216, 232, 248, 276, 279, 280] [9, 25, 41, 57, 73, 89, 105, 121, 137, 153, 169, 185, 201, 217, 233, 249, 277, 279, 280] [10, 26, 42, 58, 74, 90, 106, 122, 138, 154, 170, 186, 202, 218, 234, 250, 276, 277, 279, 280] [11, 27, 43, 59, 75, 91, 107, 123, 139, 155, 171, 187, 203, 219, 235, 251, 278, 279, 280] [12, 28, 44, 60, 76, 92, 108, 124, 140, 156, 172, 188, 204, 220, 236, 252, 276, 278, 279, 280] [13, 29, 45, 61, 77, 93, 109, 125, 141, 157, 173, 189, 205, 221, 237, 253, 277, 278, 279, 280] [14, 30, 46, 62, 78, 94, 110, 126, 142, 158, 174, 190, 206, 222, 238, 254, 276, 277, 278, 279, 280] [15, 31, 47, 63, 79, 95, 111, 127, 143, 159, 175, 191, 207, 223, 239, 255, 280]
H_Z (80 checks, sparse supports)
[0, 2, 4, 6, 8, 10, 12, 14, 256, 276] [1, 2, 5, 6, 9, 10, 13, 14, 257, 277] [3, 4, 5, 6, 11, 12, 13, 14, 258, 278] [7, 8, 9, 10, 11, 12, 13, 14, 259, 279] [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 260, 280] [16, 18, 20, 22, 24, 26, 28, 30, 261, 276] [17, 18, 21, 22, 25, 26, 29, 30, 262, 277] [19, 20, 21, 22, 27, 28, 29, 30, 263, 278] [23, 24, 25, 26, 27, 28, 29, 30, 264, 279] [16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 265, 280] [32, 34, 36, 38, 40, 42, 44, 46, 256, 261, 276] [33, 34, 37, 38, 41, 42, 45, 46, 257, 262, 277] [35, 36, 37, 38, 43, 44, 45, 46, 258, 263, 278] [39, 40, 41, 42, 43, 44, 45, 46, 259, 264, 279] [32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 260, 265, 280] [48, 50, 52, 54, 56, 58, 60, 62, 266, 276] [49, 50, 53, 54, 57, 58, 61, 62, 267, 277] [51, 52, 53, 54, 59, 60, 61, 62, 268, 278] [55, 56, 57, 58, 59, 60, 61, 62, 269, 279] [48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 270, 280] [64, 66, 68, 70, 72, 74, 76, 78, 256, 266, 276] [65, 66, 69, 70, 73, 74, 77, 78, 257, 267, 277] [67, 68, 69, 70, 75, 76, 77, 78, 258, 268, 278] [71, 72, 73, 74, 75, 76, 77, 78, 259, 269, 279] [64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 260, 270, 280] [80, 82, 84, 86, 88, 90, 92, 94, 261, 266, 276] [81, 82, 85, 86, 89, 90, 93, 94, 262, 267, 277] [83, 84, 85, 86, 91, 92, 93, 94, 263, 268, 278] [87, 88, 89, 90, 91, 92, 93, 94, 264, 269, 279] [80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 265, 270, 280] [96, 98, 100, 102, 104, 106, 108, 110, 256, 261, 266, 276] [97, 98, 101, 102, 105, 106, 109, 110, 257, 262, 267, 277] [99, 100, 101, 102, 107, 108, 109, 110, 258, 263, 268, 278] [103, 104, 105, 106, 107, 108, 109, 110, 259, 264, 269, 279] [96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 260, 265, 270, 280] [112, 114, 116, 118, 120, 122, 124, 126, 271, 276] [113, 114, 117, 118, 121, 122, 125, 126, 272, 277] [115, 116, 117, 118, 123, 124, 125, 126, 273, 278] [119, 120, 121, 122, 123, 124, 125, 126, 274, 279] [112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 275, 280] [128, 130, 132, 134, 136, 138, 140, 142, 256, 271, 276] [129, 130, 133, 134, 137, 138, 141, 142, 257, 272, 277] [131, 132, 133, 134, 139, 140, 141, 142, 258, 273, 278] [135, 136, 137, 138, 139, 140, 141, 142, 259, 274, 279] [128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 260, 275, 280] [144, 146, 148, 150, 152, 154, 156, 158, 261, 271, 276] [145, 146, 149, 150, 153, 154, 157, 158, 262, 272, 277] [147, 148, 149, 150, 155, 156, 157, 158, 263, 273, 278] [151, 152, 153, 154, 155, 156, 157, 158, 264, 274, 279] [144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 265, 275, 280] [160, 162, 164, 166, 168, 170, 172, 174, 256, 261, 271, 276] [161, 162, 165, 166, 169, 170, 173, 174, 257, 262, 272, 277] [163, 164, 165, 166, 171, 172, 173, 174, 258, 263, 273, 278] [167, 168, 169, 170, 171, 172, 173, 174, 259, 264, 274, 279] [160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 260, 265, 275, 280] [176, 178, 180, 182, 184, 186, 188, 190, 266, 271, 276] [177, 178, 181, 182, 185, 186, 189, 190, 267, 272, 277] [179, 180, 181, 182, 187, 188, 189, 190, 268, 273, 278] [183, 184, 185, 186, 187, 188, 189, 190, 269, 274, 279] [176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 270, 275, 280] [192, 194, 196, 198, 200, 202, 204, 206, 256, 266, 271, 276] [193, 194, 197, 198, 201, 202, 205, 206, 257, 267, 272, 277] [195, 196, 197, 198, 203, 204, 205, 206, 258, 268, 273, 278] [199, 200, 201, 202, 203, 204, 205, 206, 259, 269, 274, 279] [192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 260, 270, 275, 280] [208, 210, 212, 214, 216, 218, 220, 222, 261, 266, 271, 276] [209, 210, 213, 214, 217, 218, 221, 222, 262, 267, 272, 277] [211, 212, 213, 214, 219, 220, 221, 222, 263, 268, 273, 278] [215, 216, 217, 218, 219, 220, 221, 222, 264, 269, 274, 279] [208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 265, 270, 275, 280] [224, 226, 228, 230, 232, 234, 236, 238, 256, 261, 266, 271, 276] [225, 226, 229, 230, 233, 234, 237, 238, 257, 262, 267, 272, 277] [227, 228, 229, 230, 235, 236, 237, 238, 258, 263, 268, 273, 278] [231, 232, 233, 234, 235, 236, 237, 238, 259, 264, 269, 274, 279] [224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 260, 265, 270, 275, 280] [240, 242, 244, 246, 248, 250, 252, 254, 276] [241, 242, 245, 246, 249, 250, 253, 254, 277] [243, 244, 245, 246, 251, 252, 253, 254, 278] [247, 248, 249, 250, 251, 252, 253, 254, 279] [240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 280]
raw submission JSON