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[[230,46,8]] d ≤
n
230
k
46
d
8
kd²/n
12.8
w
9

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Distance

d_X 8 · witness weight 8 (claimed upper_bound)
witness operator (support, 8 qubits)
[16, 37, 41, 48, 61, 62, 66, 81]
d_Z 10 · witness weight 10 (claimed upper_bound)
witness operator (support, 10 qubits)
[55, 61, 71, 73, 80, 86, 91, 141, 142, 182]
certificate none yet · distance stands as a self-certified upper bound (d ≤)

Construction & provenance

authors @yhu1996
provenance submitted through the challenge
novelty novelty not audited
construction Mitten lifted product LP(A,B) (Bhardwaj et al arXiv:2607.28795, Def.4/8) on non-abelian group D23 (order 46): a0=[6, 12, 43], a1=[0, 28, 45], b0=[2, 5, 14], b1=[0, 10, 41] over F2[G]. n=5|G|, k=|G|, weight-9.
model Claude Claude Opus 4.8 (claimed, not verified)
builds on arXiv:2607.28795
date 2026-08-05
notes Found with Jukebox
family lifted 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 92 · Z-checks 92
H_X (92 checks, sparse supports)
[12, 17, 43, 92, 120, 126, 186, 189, 198] [13, 16, 39, 93, 124, 130, 186, 188, 202] [12, 17, 38, 94, 125, 131, 184, 185, 204] [9, 20, 35, 95, 128, 134, 188, 191, 206] [8, 21, 34, 96, 129, 135, 185, 187, 200] [13, 16, 42, 97, 121, 127, 184, 193, 208] [0, 24, 31, 98, 132, 137, 191, 195, 210] [5, 25, 30, 99, 133, 136, 187, 190, 196] [9, 20, 45, 100, 117, 123, 193, 197, 212] [8, 21, 44, 101, 116, 122, 189, 192, 194] [1, 27, 28, 102, 133, 136, 195, 199, 214] [2, 26, 29, 103, 132, 137, 190, 192, 194] [0, 24, 41, 104, 113, 119, 197, 201, 216] [5, 25, 40, 105, 112, 118, 190, 192, 196] [3, 23, 32, 106, 129, 135, 199, 203, 218] [4, 22, 33, 107, 128, 134, 189, 194, 198] [1, 28, 37, 108, 109, 115, 201, 205, 220] [2, 29, 36, 108, 109, 114, 187, 196, 200] [6, 19, 36, 110, 125, 131, 203, 207, 222] [7, 18, 37, 111, 124, 130, 186, 198, 202] [3, 32, 33, 105, 111, 112, 205, 209, 224] [4, 32, 33, 104, 110, 113, 185, 200, 204] [10, 15, 40, 114, 121, 127, 207, 211, 226] [11, 14, 41, 115, 120, 126, 188, 202, 206] [6, 29, 36, 101, 107, 116, 209, 213, 228] [7, 28, 37, 100, 106, 117, 184, 204, 208] [11, 14, 44, 117, 118, 123, 211, 215, 229] [10, 15, 45, 116, 119, 122, 191, 206, 210] [10, 25, 40, 92, 103, 120, 213, 217, 227] [11, 24, 41, 97, 102, 121, 193, 208, 212] [7, 18, 43, 113, 119, 122, 215, 219, 225] [6, 19, 42, 112, 118, 123, 195, 210, 214] [14, 21, 44, 93, 99, 124, 217, 221, 223] [15, 20, 45, 94, 98, 125, 197, 212, 216] [4, 22, 39, 109, 115, 126, 219, 221, 223] [3, 23, 38, 108, 114, 127, 199, 214, 218] [17, 18, 43, 95, 96, 128, 219, 221, 225] [16, 19, 42, 95, 96, 129, 201, 216, 220] [2, 26, 35, 105, 111, 130, 217, 223, 227] [1, 27, 34, 104, 110, 131, 203, 218, 222] [13, 22, 39, 94, 98, 132, 215, 225, 229] [12, 23, 38, 93, 99, 133, 205, 220, 224] [5, 30, 31, 101, 107, 134, 213, 227, 228] [0, 30, 31, 100, 106, 135, 207, 222, 226] [9, 26, 35, 97, 102, 136, 211, 226, 229] [8, 27, 34, 92, 103, 137, 209, 224, 228] [58, 63, 89, 138, 166, 172, 184, 194, 225] [59, 62, 85, 139, 170, 176, 185, 198, 221] [58, 63, 84, 140, 171, 177, 186, 200, 219] [55, 66, 81, 141, 174, 180, 187, 202, 217] [54, 67, 80, 142, 175, 181, 188, 196, 223] [59, 62, 88, 143, 167, 173, 189, 204, 215] [46, 70, 77, 144, 178, 183, 190, 206, 213] [51, 71, 76, 145, 179, 182, 191, 192, 227] [55, 66, 91, 146, 163, 169, 192, 208, 211] [54, 67, 90, 147, 162, 168, 190, 193, 229] [47, 73, 74, 148, 179, 182, 194, 209, 210] [48, 72, 75, 149, 178, 183, 189, 195, 228] [46, 70, 87, 150, 159, 165, 196, 207, 212] [51, 71, 86, 151, 158, 164, 187, 197, 226] [49, 69, 78, 152, 175, 181, 198, 205, 214] [50, 68, 79, 153, 174, 180, 186, 199, 224] [47, 74, 83, 154, 155, 161, 200, 203, 216] [48, 75, 82, 154, 155, 160, 185, 201, 222] [52, 65, 82, 156, 171, 177, 201, 202, 218] [53, 64, 83, 157, 170, 176, 188, 203, 220] [49, 78, 79, 151, 157, 158, 199, 204, 220] [50, 78, 79, 150, 156, 159, 184, 205, 218] [56, 61, 86, 160, 167, 173, 197, 206, 222] [57, 60, 87, 161, 166, 172, 191, 207, 216] [52, 75, 82, 147, 153, 162, 195, 208, 224] [53, 74, 83, 146, 152, 163, 193, 209, 214] [57, 60, 90, 163, 164, 169, 193, 210, 226] [56, 61, 91, 162, 165, 168, 195, 211, 212] [56, 71, 86, 138, 149, 166, 191, 212, 228] [57, 70, 87, 143, 148, 167, 197, 210, 213] [53, 64, 89, 159, 165, 168, 184, 214, 229] [52, 65, 88, 158, 164, 169, 199, 208, 215] [60, 67, 90, 139, 145, 170, 188, 216, 227] [61, 66, 91, 140, 144, 171, 201, 206, 217] [50, 68, 85, 155, 161, 172, 185, 218, 225] [49, 69, 84, 154, 160, 173, 203, 204, 219] [63, 64, 89, 141, 142, 174, 186, 220, 223] [62, 65, 88, 141, 142, 175, 202, 205, 221] [48, 72, 81, 151, 157, 176, 187, 221, 222] [47, 73, 80, 150, 156, 177, 200, 207, 223] [59, 68, 85, 140, 144, 178, 189, 219, 224] [58, 69, 84, 139, 145, 179, 198, 209, 225] [51, 76, 77, 147, 153, 180, 190, 217, 226] [46, 76, 77, 146, 152, 181, 196, 211, 227] [55, 72, 81, 143, 148, 182, 192, 215, 228] [54, 73, 80, 138, 149, 183, 194, 213, 229]
H_Z (92 checks, sparse supports)
[2, 5, 25, 46, 67, 76, 190, 196, 227] [2, 4, 21, 47, 63, 80, 194, 200, 223] [0, 1, 19, 48, 61, 82, 195, 201, 222] [4, 7, 17, 49, 59, 84, 198, 204, 219] [1, 3, 23, 50, 65, 78, 199, 205, 218] [0, 9, 15, 51, 57, 86, 191, 197, 226] [7, 11, 13, 52, 55, 88, 202, 208, 215] [3, 6, 27, 53, 69, 74, 203, 209, 214] [9, 11, 13, 53, 54, 90, 188, 193, 229] [5, 8, 29, 55, 71, 72, 187, 192, 228] [9, 11, 15, 46, 56, 91, 206, 211, 212] [6, 10, 31, 57, 70, 73, 207, 210, 213] [7, 13, 17, 50, 58, 89, 184, 186, 225] [8, 12, 33, 59, 68, 75, 185, 189, 224] [0, 15, 19, 47, 60, 87, 207, 210, 216] [10, 14, 35, 61, 66, 77, 206, 211, 217] [4, 17, 21, 48, 62, 85, 185, 189, 221] [12, 16, 37, 63, 64, 79, 184, 186, 220] [1, 19, 23, 49, 64, 83, 203, 214, 220] [14, 18, 39, 62, 65, 81, 202, 215, 221] [2, 21, 25, 51, 66, 81, 187, 192, 217] [16, 20, 41, 60, 67, 83, 188, 193, 216] [3, 23, 27, 52, 68, 79, 199, 218, 224] [18, 22, 43, 58, 69, 85, 198, 219, 225] [5, 25, 29, 54, 70, 77, 190, 196, 213] [20, 24, 45, 56, 71, 87, 191, 197, 212] [6, 27, 31, 56, 72, 75, 195, 222, 228] [22, 26, 44, 54, 73, 89, 194, 223, 229] [8, 29, 33, 58, 73, 74, 194, 200, 209] [24, 28, 42, 52, 75, 91, 195, 201, 208] [10, 31, 35, 60, 71, 76, 191, 226, 227] [26, 30, 40, 51, 77, 90, 190, 226, 227] [12, 33, 37, 62, 69, 78, 198, 204, 205] [28, 32, 38, 49, 79, 88, 199, 204, 205] [14, 35, 39, 64, 67, 80, 188, 223, 229] [30, 34, 36, 48, 81, 86, 187, 222, 228] [16, 37, 41, 65, 66, 82, 201, 202, 208] [32, 34, 36, 47, 83, 84, 200, 203, 209] [18, 39, 43, 63, 68, 84, 186, 219, 225] [32, 34, 38, 50, 82, 85, 185, 218, 224] [20, 41, 45, 61, 70, 86, 197, 206, 212] [30, 36, 40, 46, 80, 87, 196, 207, 213] [22, 43, 44, 59, 72, 88, 189, 215, 221] [28, 38, 42, 53, 78, 89, 184, 214, 220] [24, 42, 45, 57, 74, 90, 193, 210, 216] [26, 40, 44, 55, 76, 91, 192, 211, 217] [94, 97, 117, 138, 159, 168, 184, 212, 229] [94, 96, 113, 139, 155, 172, 185, 216, 225] [92, 93, 111, 140, 153, 174, 186, 217, 224] [96, 99, 109, 141, 151, 176, 187, 220, 221] [93, 95, 115, 142, 157, 170, 188, 220, 221] [92, 101, 107, 143, 149, 178, 189, 213, 228] [99, 103, 105, 144, 147, 180, 190, 217, 224] [95, 98, 119, 145, 161, 166, 191, 216, 225] [101, 103, 105, 145, 146, 182, 192, 209, 227] [97, 100, 121, 147, 163, 164, 193, 208, 226] [101, 103, 107, 138, 148, 183, 194, 213, 228] [98, 102, 123, 149, 162, 165, 195, 212, 229] [99, 105, 109, 142, 150, 181, 196, 205, 223] [100, 104, 125, 151, 160, 167, 197, 204, 222] [92, 107, 111, 139, 152, 179, 198, 209, 227] [102, 106, 127, 153, 158, 169, 199, 208, 226] [96, 109, 113, 140, 154, 177, 200, 201, 219] [104, 108, 129, 155, 156, 171, 200, 201, 218] [93, 111, 115, 141, 156, 175, 202, 205, 223] [106, 110, 131, 154, 157, 173, 203, 204, 222] [94, 113, 117, 143, 158, 173, 197, 204, 215] [108, 112, 133, 152, 159, 175, 196, 205, 214] [95, 115, 119, 144, 160, 171, 201, 206, 219] [110, 114, 135, 150, 161, 177, 200, 207, 218] [97, 117, 121, 146, 162, 169, 193, 208, 211] [112, 116, 137, 148, 163, 179, 192, 209, 210] [98, 119, 123, 148, 164, 167, 197, 210, 215] [114, 118, 136, 146, 165, 181, 196, 211, 214] [100, 121, 125, 150, 165, 166, 184, 207, 212] [116, 120, 134, 144, 167, 183, 189, 206, 213] [102, 123, 127, 152, 163, 168, 193, 211, 214] [118, 122, 132, 143, 169, 182, 192, 210, 215] [104, 125, 129, 154, 161, 170, 185, 203, 216] [120, 124, 130, 141, 171, 180, 186, 202, 217] [106, 127, 131, 156, 159, 172, 184, 207, 218] [122, 126, 128, 140, 173, 178, 189, 206, 219] [108, 129, 133, 157, 158, 174, 187, 199, 220] [124, 126, 128, 139, 175, 176, 188, 198, 221] [110, 131, 135, 155, 160, 176, 185, 203, 222] [124, 126, 130, 142, 174, 177, 186, 202, 223] [112, 133, 137, 153, 162, 178, 190, 195, 224] [122, 128, 132, 138, 172, 179, 191, 194, 225] [114, 135, 136, 151, 164, 180, 187, 199, 226] [120, 130, 134, 145, 170, 181, 188, 198, 227] [116, 134, 137, 149, 166, 182, 191, 194, 228] [118, 132, 136, 147, 168, 183, 190, 195, 229]
raw submission JSON