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[[220,44,10]] d ≤
n
220
k
44
d
10
kd²/n
20.0
w
9

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Distance

d_X 10 · witness weight 10 (claimed upper_bound)
witness operator (support, 10 qubits)
[16, 18, 23, 40, 51, 53, 54, 58, 73, 78]
d_Z 10 · witness weight 10 (claimed upper_bound)
witness operator (support, 10 qubits)
[5, 6, 28, 90, 100, 103, 104, 108, 123, 126]
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 metacyclic(C11:C4,r=10) (order 44): a0=[10, 23, 42], a1=[0, 15, 33], b0=[16, 22, 29], b1=[0, 4, 43] 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 88 · Z-checks 88
H_X (88 checks, sparse supports)
[6, 21, 38, 88, 101, 123, 192, 198, 205] [7, 22, 39, 89, 102, 120, 194, 203, 205] [4, 23, 36, 90, 103, 121, 194, 196, 207] [5, 20, 37, 91, 100, 122, 192, 201, 207] [10, 17, 42, 92, 97, 119, 196, 202, 209] [11, 18, 43, 93, 98, 116, 198, 207, 209] [8, 19, 40, 94, 99, 117, 198, 200, 211] [9, 16, 41, 95, 96, 118, 196, 205, 211] [2, 13, 14, 93, 96, 115, 200, 206, 213] [3, 14, 15, 94, 97, 112, 202, 211, 213] [0, 12, 15, 95, 98, 113, 202, 204, 215] [1, 12, 13, 92, 99, 114, 200, 209, 215] [6, 9, 18, 89, 100, 111, 204, 210, 217] [7, 10, 19, 90, 101, 108, 206, 215, 217] [4, 11, 16, 91, 102, 109, 206, 208, 219] [5, 8, 17, 88, 103, 110, 204, 213, 219] [5, 10, 22, 104, 107, 129, 177, 208, 214] [6, 11, 23, 104, 105, 130, 177, 210, 219] [7, 8, 20, 105, 106, 131, 179, 210, 212] [4, 9, 21, 106, 107, 128, 179, 208, 217] [1, 14, 26, 103, 108, 125, 181, 212, 218] [2, 15, 27, 100, 109, 126, 179, 181, 214] [3, 12, 24, 101, 110, 127, 183, 214, 216] [0, 13, 25, 102, 111, 124, 177, 183, 212] [18, 30, 41, 99, 112, 121, 178, 185, 216] [19, 31, 42, 96, 113, 122, 183, 185, 218] [16, 28, 43, 97, 114, 123, 176, 187, 218] [17, 29, 40, 98, 115, 120, 181, 187, 216] [22, 34, 37, 95, 116, 117, 176, 182, 189] [23, 35, 38, 92, 117, 118, 178, 187, 189] [20, 32, 39, 93, 118, 119, 178, 180, 191] [21, 33, 36, 94, 116, 119, 176, 185, 191] [26, 33, 38, 91, 113, 120, 180, 186, 193] [27, 34, 39, 88, 114, 121, 182, 191, 193] [24, 35, 36, 89, 115, 122, 182, 184, 195] [25, 32, 37, 90, 112, 123, 180, 189, 195] [29, 30, 42, 109, 124, 131, 184, 190, 197] [30, 31, 43, 110, 125, 128, 186, 195, 197] [28, 31, 40, 111, 126, 129, 186, 188, 199] [28, 29, 41, 108, 127, 130, 184, 193, 199] [2, 25, 34, 105, 127, 128, 188, 194, 201] [3, 26, 35, 106, 124, 129, 190, 199, 201] [0, 27, 32, 107, 125, 130, 190, 192, 203] [1, 24, 33, 104, 126, 131, 188, 197, 203] [50, 65, 82, 132, 145, 167, 176, 180, 219] [51, 66, 83, 133, 146, 164, 177, 180, 217] [48, 67, 80, 134, 147, 165, 178, 182, 217] [49, 64, 81, 135, 144, 166, 179, 182, 219] [54, 61, 86, 136, 141, 163, 179, 180, 184] [55, 62, 87, 137, 142, 160, 177, 181, 184] [52, 63, 84, 138, 143, 161, 177, 182, 186] [53, 60, 85, 139, 140, 162, 179, 183, 186] [46, 57, 58, 137, 140, 159, 183, 184, 188] [47, 58, 59, 138, 141, 156, 181, 185, 188] [44, 56, 59, 139, 142, 157, 181, 186, 190] [45, 56, 57, 136, 143, 158, 183, 187, 190] [50, 53, 62, 133, 144, 155, 187, 188, 192] [51, 54, 63, 134, 145, 152, 185, 189, 192] [48, 55, 60, 135, 146, 153, 185, 190, 194] [49, 52, 61, 132, 147, 154, 187, 191, 194] [49, 54, 66, 148, 151, 173, 191, 192, 196] [50, 55, 67, 148, 149, 174, 189, 193, 196] [51, 52, 64, 149, 150, 175, 189, 194, 198] [48, 53, 65, 150, 151, 172, 191, 195, 198] [45, 58, 70, 147, 152, 169, 195, 196, 200] [46, 59, 71, 144, 153, 170, 193, 197, 200] [47, 56, 68, 145, 154, 171, 193, 198, 202] [44, 57, 69, 146, 155, 168, 195, 199, 202] [62, 74, 85, 143, 156, 165, 199, 200, 204] [63, 75, 86, 140, 157, 166, 197, 201, 204] [60, 72, 87, 141, 158, 167, 197, 202, 206] [61, 73, 84, 142, 159, 164, 199, 203, 206] [66, 78, 81, 139, 160, 161, 203, 204, 208] [67, 79, 82, 136, 161, 162, 201, 205, 208] [64, 76, 83, 137, 162, 163, 201, 206, 210] [65, 77, 80, 138, 160, 163, 203, 207, 210] [70, 77, 82, 135, 157, 164, 207, 208, 212] [71, 78, 83, 132, 158, 165, 205, 209, 212] [68, 79, 80, 133, 159, 166, 205, 210, 214] [69, 76, 81, 134, 156, 167, 207, 211, 214] [73, 74, 86, 153, 168, 175, 211, 212, 216] [74, 75, 87, 154, 169, 172, 209, 213, 216] [72, 75, 84, 155, 170, 173, 209, 214, 218] [72, 73, 85, 152, 171, 174, 211, 215, 218] [46, 69, 78, 149, 171, 172, 176, 215, 216] [47, 70, 79, 150, 168, 173, 176, 213, 217] [44, 71, 76, 151, 169, 174, 178, 213, 218] [45, 68, 77, 148, 170, 175, 178, 215, 219]
H_Z (88 checks, sparse supports)
[26, 28, 31, 44, 84, 85, 186, 199, 218] [16, 17, 23, 45, 49, 50, 187, 196, 219] [24, 29, 30, 46, 86, 87, 184, 197, 216] [18, 19, 21, 47, 48, 51, 185, 198, 217] [30, 32, 35, 44, 45, 48, 178, 190, 195] [20, 21, 27, 49, 53, 54, 179, 191, 192] [28, 33, 34, 46, 47, 50, 176, 188, 193] [22, 23, 25, 51, 52, 55, 177, 189, 194] [34, 36, 39, 48, 49, 52, 182, 191, 194] [24, 25, 31, 53, 57, 58, 183, 188, 195] [32, 37, 38, 50, 51, 54, 180, 189, 192] [26, 27, 29, 55, 56, 59, 181, 190, 193] [38, 40, 43, 52, 53, 56, 186, 187, 198] [28, 29, 35, 57, 61, 62, 184, 187, 199] [36, 41, 42, 54, 55, 58, 184, 185, 196] [30, 31, 33, 59, 60, 63, 185, 186, 197] [0, 3, 42, 56, 57, 60, 183, 190, 202] [32, 33, 39, 61, 65, 66, 180, 191, 203] [1, 2, 40, 58, 59, 62, 181, 188, 200] [34, 35, 37, 63, 64, 67, 182, 189, 201] [2, 4, 7, 60, 61, 64, 179, 194, 206] [36, 37, 43, 65, 69, 70, 176, 195, 207] [0, 5, 6, 62, 63, 66, 177, 192, 204] [38, 39, 41, 67, 68, 71, 178, 193, 205] [6, 8, 11, 64, 65, 68, 198, 210, 219] [3, 40, 41, 69, 73, 74, 199, 211, 216] [4, 9, 10, 66, 67, 70, 196, 208, 217] [1, 42, 43, 71, 72, 75, 197, 209, 218] [10, 12, 15, 68, 69, 72, 202, 214, 215] [0, 1, 7, 73, 77, 78, 203, 212, 215] [8, 13, 14, 70, 71, 74, 200, 212, 213] [2, 3, 5, 75, 76, 79, 201, 213, 214] [14, 16, 19, 72, 73, 76, 206, 211, 218] [4, 5, 11, 77, 81, 82, 207, 208, 219] [12, 17, 18, 74, 75, 78, 204, 209, 216] [6, 7, 9, 79, 80, 83, 205, 210, 217] [18, 20, 23, 76, 77, 80, 178, 207, 210] [8, 9, 15, 81, 85, 86, 179, 204, 211] [16, 21, 22, 78, 79, 82, 176, 205, 208] [10, 11, 13, 83, 84, 87, 177, 206, 209] [22, 24, 27, 80, 81, 84, 182, 203, 214] [12, 13, 19, 45, 46, 85, 183, 200, 215] [20, 25, 26, 82, 83, 86, 180, 201, 212] [14, 15, 17, 44, 47, 87, 181, 202, 213] [114, 116, 119, 132, 172, 173, 176, 191, 209] [104, 105, 111, 133, 137, 138, 177, 188, 210] [112, 117, 118, 134, 174, 175, 178, 189, 211] [106, 107, 109, 135, 136, 139, 179, 190, 208] [118, 120, 123, 132, 133, 136, 180, 187, 205] [108, 109, 115, 137, 141, 142, 181, 184, 206] [116, 121, 122, 134, 135, 138, 182, 185, 207] [110, 111, 113, 139, 140, 143, 183, 186, 204] [122, 124, 127, 136, 137, 140, 183, 184, 201] [112, 113, 119, 141, 145, 146, 180, 185, 202] [120, 125, 126, 138, 139, 142, 181, 186, 203] [114, 115, 117, 143, 144, 147, 182, 187, 200] [126, 128, 131, 140, 141, 144, 179, 188, 197] [116, 117, 123, 145, 149, 150, 176, 189, 198] [124, 129, 130, 142, 143, 146, 177, 190, 199] [118, 119, 121, 147, 148, 151, 178, 191, 196] [88, 91, 130, 144, 145, 148, 192, 193, 219] [120, 121, 127, 149, 153, 154, 193, 194, 216] [89, 90, 128, 146, 147, 150, 194, 195, 217] [122, 123, 125, 151, 152, 155, 192, 195, 218] [90, 92, 95, 148, 149, 152, 189, 196, 215] [124, 125, 131, 153, 157, 158, 190, 197, 212] [88, 93, 94, 150, 151, 154, 191, 198, 213] [126, 127, 129, 155, 156, 159, 188, 199, 214] [94, 96, 99, 152, 153, 156, 185, 200, 211] [91, 128, 129, 157, 161, 162, 186, 201, 208] [92, 97, 98, 154, 155, 158, 187, 202, 209] [89, 130, 131, 159, 160, 163, 184, 203, 210] [98, 100, 103, 156, 157, 160, 181, 204, 207] [88, 89, 95, 161, 165, 166, 182, 204, 205] [96, 101, 102, 158, 159, 162, 183, 205, 206] [90, 91, 93, 163, 164, 167, 180, 206, 207] [102, 104, 107, 160, 161, 164, 177, 203, 208] [92, 93, 99, 165, 169, 170, 178, 200, 209] [100, 105, 106, 162, 163, 166, 179, 201, 210] [94, 95, 97, 167, 168, 171, 176, 202, 211] [106, 108, 111, 164, 165, 168, 199, 212, 217] [96, 97, 103, 169, 173, 174, 196, 213, 218] [104, 109, 110, 166, 167, 170, 197, 214, 219] [98, 99, 101, 171, 172, 175, 198, 215, 216] [110, 112, 115, 168, 169, 172, 195, 213, 216] [100, 101, 107, 133, 134, 173, 192, 214, 217] [108, 113, 114, 170, 171, 174, 193, 215, 218] [102, 103, 105, 132, 135, 175, 194, 212, 219]
raw submission JSON