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[[180,6,10]] d =
n
180
k
6
d
10
kd²/n
3.333
w
6
g
0.0115
r
4.1231
layers
2

Share this result

Distance

d_X 10 · witness weight 10 (claimed exact)
witness operator (support, 10 qubits)
[4, 36, 56, 65, 75, 105, 136, 145, 155, 156]
d_Z 10 · witness weight 10 (claimed exact)
witness operator (support, 10 qubits)
[29, 31, 33, 35, 37, 39, 121, 123, 125, 127]
certificate exact, d = 10 · scipy/HiGHS cutoff IP
X: no logical < 10 exists; Z: no logical < 10 exists

Verified 2D layout

as measured by the verifier: every check drawn over the submitted coordinates; the interaction radius is the longest dashed pair
r = 4.123
X checkZ checkqubit site (90)2 qubits stacked (2 layers)dashed: the pair setting the interaction radiushover a check to isolate its qubits; click to pin — repeated clicks cycle through overlapping checks; click empty space to release

Construction & provenance

authors @FarLab and @vprusso
provenance submitted through the challenge
novelty novelty not audited
construction f = 1 + xy + x-1 y2, g = 1 + x-1 y + x-2 y-1; annulus-type boundary engine, (9,10) lattice.
model Claude Claude Opus 4.8 (claimed, not verified)
builds on arXiv:2504.08887
date 2026-06-16
family bivariate bicycle (a tag, not a ranking)
locality 2D-local bilayer (computed from the layout)
weight class weight ≤ 6 (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 96 · Z-checks 95
H_X (96 checks, sparse supports)
[2, 10, 21, 90, 102, 111] [3, 11, 22, 91, 103, 112] [4, 12, 23, 92, 104, 113] [5, 13, 24, 93, 105, 114] [6, 14, 25, 94, 106, 115] [7, 15, 26, 95, 107, 116] [8, 16, 27, 96, 108, 117] [9, 17, 28, 97, 109, 118] [12, 20, 31, 100, 112, 121] [13, 21, 32, 101, 113, 122] [14, 22, 33, 102, 114, 123] [15, 23, 34, 103, 115, 124] [16, 24, 35, 104, 116, 125] [17, 25, 36, 105, 117, 126] [18, 26, 37, 106, 118, 127] [19, 27, 38, 107, 119, 128] [22, 30, 41, 110, 122, 131] [23, 31, 42, 111, 123, 132] [24, 32, 43, 112, 124, 133] [25, 33, 44, 113, 125, 134] [26, 34, 45, 114, 126, 135] [27, 35, 46, 115, 127, 136] [28, 36, 47, 116, 128, 137] [29, 37, 48, 117, 129, 138] [32, 40, 51, 120, 132, 141] [33, 41, 52, 121, 133, 142] [34, 42, 53, 122, 134, 143] [35, 43, 54, 123, 135, 144] [36, 44, 55, 124, 136, 145] [37, 45, 56, 125, 137, 146] [38, 46, 57, 126, 138, 147] [39, 47, 58, 127, 139, 148] [42, 50, 61, 130, 142, 151] [43, 51, 62, 131, 143, 152] [44, 52, 63, 132, 144, 153] [45, 53, 64, 133, 145, 154] [46, 54, 65, 134, 146, 155] [47, 55, 66, 135, 147, 156] [48, 56, 67, 136, 148, 157] [49, 57, 68, 137, 149, 158] [52, 60, 71, 140, 152, 161] [53, 61, 72, 141, 153, 162] [54, 62, 73, 142, 154, 163] [55, 63, 74, 143, 155, 164] [56, 64, 75, 144, 156, 165] [57, 65, 76, 145, 157, 166] [58, 66, 77, 146, 158, 167] [59, 67, 78, 147, 159, 168] [62, 70, 81, 150, 162, 171] [63, 71, 82, 151, 163, 172] [64, 72, 83, 152, 164, 173] [65, 73, 84, 153, 165, 174] [66, 74, 85, 154, 166, 175] [67, 75, 86, 155, 167, 176] [68, 76, 87, 156, 168, 177] [69, 77, 88, 157, 169, 178] [0, 90] [1, 91] [2, 92] [3, 93] [4, 94] [5, 95] [6, 96] [7, 97] [8, 98] [9, 99] [82, 170] [83, 171] [84, 172] [85, 173] [86, 174] [87, 175] [88, 176] [89, 177] [11, 90, 92, 101] [12, 91, 93, 102] [13, 92, 94, 103] [14, 93, 95, 104] [15, 94, 96, 105] [16, 95, 97, 106] [17, 96, 98, 107] [18, 97, 99, 108] [74, 162, 170, 174] [75, 163, 171, 175] [76, 164, 172, 176] [77, 165, 173, 177] [78, 166, 174, 178] [79, 167, 175, 179] [72, 80, 160, 172] [73, 81, 161, 173] [74, 82, 162, 174] [75, 83, 163, 175] [76, 84, 164, 176] [77, 85, 165, 177] [78, 86, 166, 178] [79, 87, 167, 179]
H_Z (95 checks, sparse supports)
[1, 10, 22, 91, 102, 110] [2, 11, 23, 92, 103, 111] [3, 12, 24, 93, 104, 112] [4, 13, 25, 94, 105, 113] [5, 14, 26, 95, 106, 114] [6, 15, 27, 96, 107, 115] [7, 16, 28, 97, 108, 116] [8, 17, 29, 98, 109, 117] [11, 20, 32, 101, 112, 120] [12, 21, 33, 102, 113, 121] [13, 22, 34, 103, 114, 122] [14, 23, 35, 104, 115, 123] [15, 24, 36, 105, 116, 124] [16, 25, 37, 106, 117, 125] [17, 26, 38, 107, 118, 126] [18, 27, 39, 108, 119, 127] [21, 30, 42, 111, 122, 130] [22, 31, 43, 112, 123, 131] [23, 32, 44, 113, 124, 132] [24, 33, 45, 114, 125, 133] [25, 34, 46, 115, 126, 134] [26, 35, 47, 116, 127, 135] [27, 36, 48, 117, 128, 136] [28, 37, 49, 118, 129, 137] [31, 40, 52, 121, 132, 140] [32, 41, 53, 122, 133, 141] [33, 42, 54, 123, 134, 142] [34, 43, 55, 124, 135, 143] [35, 44, 56, 125, 136, 144] [36, 45, 57, 126, 137, 145] [37, 46, 58, 127, 138, 146] [38, 47, 59, 128, 139, 147] [41, 50, 62, 131, 142, 150] [42, 51, 63, 132, 143, 151] [43, 52, 64, 133, 144, 152] [44, 53, 65, 134, 145, 153] [45, 54, 66, 135, 146, 154] [46, 55, 67, 136, 147, 155] [47, 56, 68, 137, 148, 156] [48, 57, 69, 138, 149, 157] [51, 60, 72, 141, 152, 160] [52, 61, 73, 142, 153, 161] [53, 62, 74, 143, 154, 162] [54, 63, 75, 144, 155, 163] [55, 64, 76, 145, 156, 164] [56, 65, 77, 146, 157, 165] [57, 66, 78, 147, 158, 166] [58, 67, 79, 148, 159, 167] [61, 70, 82, 151, 162, 170] [62, 71, 83, 152, 163, 171] [63, 72, 84, 153, 164, 172] [64, 73, 85, 154, 165, 173] [65, 74, 86, 155, 166, 174] [66, 75, 87, 156, 167, 175] [67, 76, 88, 157, 168, 176] [68, 77, 89, 158, 169, 177] [20, 100] [30, 110] [40, 120] [50, 130] [60, 140] [70, 150] [80, 160] [19, 119] [29, 129] [39, 139] [49, 149] [59, 159] [69, 169] [79, 179] [41, 100, 110, 121] [51, 110, 120, 131] [61, 120, 130, 141] [71, 130, 140, 151] [81, 140, 150, 161] [0, 21, 90, 101] [10, 31, 100, 111] [20, 41, 110, 121] [30, 51, 120, 131] [40, 61, 130, 141] [50, 71, 140, 151] [60, 81, 150, 161] [28, 109, 119, 128] [38, 119, 129, 138] [48, 129, 139, 148] [58, 139, 149, 158] [68, 149, 159, 168] [78, 159, 169, 178] [9, 18, 99, 118] [19, 28, 109, 128] [29, 38, 119, 138] [39, 48, 129, 148] [49, 58, 139, 158] [59, 68, 149, 168] [69, 78, 159, 178]
raw submission JSON