← back to the board
[[231,5,11]] d =
n
231
k
5
d
11
kd²/n
2.619
w
6
g
0.0262
r
3.1623
layers
2

Share this result

Distance

d_X 11 · witness weight 11 (claimed exact)
witness operator (support, 11 qubits)
[8, 40, 62, 72, 105, 128, 151, 162, 172, 204, 216]
d_Z 11 · witness weight 11 (claimed exact)
witness operator (support, 11 qubits)
[64, 70, 173, 174, 179, 182, 188, 189, 190, 191, 192]
certificate exact, d = 11 · scipy/HiGHS MILP
X: no logical < 11 exists; Z: no logical < 11 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 = 3.162
X checkZ checkqubit site (121)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 Generalized weight-6, (11,11) open-boundary lattice. New instance of the Liang-Eberhardt-Chen open-boundary family (arXiv:2504.08887); the paper has no k=5 family.
model Claude Claude Opus 4.8 (claimed, not verified)
builds on arXiv:2504.08887
date 2026-06-19
notes Distance proven exact by cutoff MILP (scipy/HiGHS); no lighter logical exists on either side. 2D-local bilayer layout (reconstructed 2026-07-02): A/B sublattices of 11x11 and 10x11 rows on one grid, physical row = (+i+1) mod 11 on A and (+i+0) mod 10 on B; interaction radius 3.162.
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 109 · Z-checks 123
H_X (109 checks, sparse supports)
[0, 12, 23, 122, 123, 132] [1, 13, 24, 123, 124, 133] [2, 14, 25, 124, 125, 134] [3, 15, 26, 125, 126, 135] [4, 16, 27, 126, 127, 136] [5, 17, 28, 127, 128, 137] [6, 18, 29, 128, 129, 138] [7, 19, 30, 129, 130, 139] [8, 20, 31, 130, 131, 140] [11, 23, 34, 133, 134, 143] [12, 24, 35, 134, 135, 144] [13, 25, 36, 135, 136, 145] [14, 26, 37, 136, 137, 146] [15, 27, 38, 137, 138, 147] [16, 28, 39, 138, 139, 148] [17, 29, 40, 139, 140, 149] [18, 30, 41, 140, 141, 150] [19, 31, 42, 141, 142, 151] [22, 34, 45, 144, 145, 154] [23, 35, 46, 145, 146, 155] [24, 36, 47, 146, 147, 156] [25, 37, 48, 147, 148, 157] [26, 38, 49, 148, 149, 158] [27, 39, 50, 149, 150, 159] [28, 40, 51, 150, 151, 160] [29, 41, 52, 151, 152, 161] [30, 42, 53, 152, 153, 162] [33, 45, 56, 155, 156, 165] [34, 46, 57, 156, 157, 166] [35, 47, 58, 157, 158, 167] [36, 48, 59, 158, 159, 168] [37, 49, 60, 159, 160, 169] [38, 50, 61, 160, 161, 170] [39, 51, 62, 161, 162, 171] [40, 52, 63, 162, 163, 172] [41, 53, 64, 163, 164, 173] [44, 56, 67, 166, 167, 176] [45, 57, 68, 167, 168, 177] [46, 58, 69, 168, 169, 178] [47, 59, 70, 169, 170, 179] [48, 60, 71, 170, 171, 180] [49, 61, 72, 171, 172, 181] [50, 62, 73, 172, 173, 182] [51, 63, 74, 173, 174, 183] [52, 64, 75, 174, 175, 184] [55, 67, 78, 177, 178, 187] [56, 68, 79, 178, 179, 188] [57, 69, 80, 179, 180, 189] [58, 70, 81, 180, 181, 190] [59, 71, 82, 181, 182, 191] [60, 72, 83, 182, 183, 192] [61, 73, 84, 183, 184, 193] [62, 74, 85, 184, 185, 194] [63, 75, 86, 185, 186, 195] [66, 78, 89, 188, 189, 198] [67, 79, 90, 189, 190, 199] [68, 80, 91, 190, 191, 200] [69, 81, 92, 191, 192, 201] [70, 82, 93, 192, 193, 202] [71, 83, 94, 193, 194, 203] [72, 84, 95, 194, 195, 204] [73, 85, 96, 195, 196, 205] [74, 86, 97, 196, 197, 206] [77, 89, 100, 199, 200, 209] [78, 90, 101, 200, 201, 210] [79, 91, 102, 201, 202, 211] [80, 92, 103, 202, 203, 212] [81, 93, 104, 203, 204, 213] [82, 94, 105, 204, 205, 214] [83, 95, 106, 205, 206, 215] [84, 96, 107, 206, 207, 216] [85, 97, 108, 207, 208, 217] [1, 110] [2, 111] [3, 112] [4, 113] [5, 114] [6, 115] [7, 116] [8, 117] [9, 118] [10, 119] [99, 221, 222] [100, 222, 223] [101, 223, 224] [102, 224, 225] [103, 225, 226] [104, 226, 227] [105, 227, 228] [106, 228, 229] [107, 229, 230] [12, 110, 111, 112, 121] [13, 111, 112, 113, 122] [14, 112, 113, 114, 123] [15, 113, 114, 115, 124] [16, 114, 115, 116, 125] [17, 115, 116, 117, 126] [18, 116, 117, 118, 127] [19, 117, 118, 119, 128] [20, 118, 119, 120, 129] [88, 100, 210, 211, 220] [89, 101, 211, 212, 221] [90, 102, 212, 213, 222] [91, 103, 213, 214, 223] [92, 104, 214, 215, 224] [93, 105, 215, 216, 225] [94, 106, 216, 217, 226] [95, 107, 217, 218, 227] [96, 108, 218, 219, 228]
H_Z (123 checks, sparse supports)
[2, 11, 12, 111, 122, 134] [3, 12, 13, 112, 123, 135] [4, 13, 14, 113, 124, 136] [5, 14, 15, 114, 125, 137] [6, 15, 16, 115, 126, 138] [7, 16, 17, 116, 127, 139] [8, 17, 18, 117, 128, 140] [9, 18, 19, 118, 129, 141] [10, 19, 20, 119, 130, 142] [13, 22, 23, 122, 133, 145] [14, 23, 24, 123, 134, 146] [15, 24, 25, 124, 135, 147] [16, 25, 26, 125, 136, 148] [17, 26, 27, 126, 137, 149] [18, 27, 28, 127, 138, 150] [19, 28, 29, 128, 139, 151] [20, 29, 30, 129, 140, 152] [21, 30, 31, 130, 141, 153] [24, 33, 34, 133, 144, 156] [25, 34, 35, 134, 145, 157] [26, 35, 36, 135, 146, 158] [27, 36, 37, 136, 147, 159] [28, 37, 38, 137, 148, 160] [29, 38, 39, 138, 149, 161] [30, 39, 40, 139, 150, 162] [31, 40, 41, 140, 151, 163] [32, 41, 42, 141, 152, 164] [35, 44, 45, 144, 155, 167] [36, 45, 46, 145, 156, 168] [37, 46, 47, 146, 157, 169] [38, 47, 48, 147, 158, 170] [39, 48, 49, 148, 159, 171] [40, 49, 50, 149, 160, 172] [41, 50, 51, 150, 161, 173] [42, 51, 52, 151, 162, 174] [43, 52, 53, 152, 163, 175] [46, 55, 56, 155, 166, 178] [47, 56, 57, 156, 167, 179] [48, 57, 58, 157, 168, 180] [49, 58, 59, 158, 169, 181] [50, 59, 60, 159, 170, 182] [51, 60, 61, 160, 171, 183] [52, 61, 62, 161, 172, 184] [53, 62, 63, 162, 173, 185] [54, 63, 64, 163, 174, 186] [57, 66, 67, 166, 177, 189] [58, 67, 68, 167, 178, 190] [59, 68, 69, 168, 179, 191] [60, 69, 70, 169, 180, 192] [61, 70, 71, 170, 181, 193] [62, 71, 72, 171, 182, 194] [63, 72, 73, 172, 183, 195] [64, 73, 74, 173, 184, 196] [65, 74, 75, 174, 185, 197] [68, 77, 78, 177, 188, 200] [69, 78, 79, 178, 189, 201] [70, 79, 80, 179, 190, 202] [71, 80, 81, 180, 191, 203] [72, 81, 82, 181, 192, 204] [73, 82, 83, 182, 193, 205] [74, 83, 84, 183, 194, 206] [75, 84, 85, 184, 195, 207] [76, 85, 86, 185, 196, 208] [79, 88, 89, 188, 199, 211] [80, 89, 90, 189, 200, 212] [81, 90, 91, 190, 201, 213] [82, 91, 92, 191, 202, 214] [83, 92, 93, 192, 203, 215] [84, 93, 94, 193, 204, 216] [85, 94, 95, 194, 205, 217] [86, 95, 96, 195, 206, 218] [87, 96, 97, 196, 207, 219] [90, 99, 100, 199, 210, 222] [91, 100, 101, 200, 211, 223] [92, 101, 102, 201, 212, 224] [93, 102, 103, 202, 213, 225] [94, 103, 104, 203, 214, 226] [95, 104, 105, 204, 215, 227] [96, 105, 106, 205, 216, 228] [97, 106, 107, 206, 217, 229] [98, 107, 108, 207, 218, 230] [21] [32] [43] [54] [65] [76] [87] [98] [109] [0, 132] [11, 143] [22, 154] [33, 165] [44, 176] [55, 187] [66, 198] [77, 209] [88, 220] [20, 120, 131] [31, 131, 142] [42, 142, 153] [53, 153, 164] [64, 164, 175] [75, 175, 186] [86, 186, 197] [97, 197, 208] [108, 208, 219] [1, 110, 121, 133, 143] [12, 121, 132, 144, 154] [23, 132, 143, 155, 165] [34, 143, 154, 166, 176] [45, 154, 165, 177, 187] [56, 165, 176, 188, 198] [67, 176, 187, 199, 209] [78, 187, 198, 210, 220] [0, 11, 23, 33, 155] [11, 22, 34, 44, 166] [22, 33, 45, 55, 177] [33, 44, 56, 66, 188] [44, 55, 67, 77, 199] [55, 66, 78, 88, 210] [66, 77, 89, 99, 221]
raw submission JSON