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[[288,8,12]] d =
n
288
k
8
d
12
kd²/n
4.0
w
6
g
0.0625
r
2.8284
layers
2

Share this result

Distance

d_X 12 · witness weight 12 (claimed upper_bound)
witness operator (support, 12 qubits)
[36, 61, 62, 96, 121, 144, 156, 228, 230, 240, 252, 264]
d_Z 12 · witness weight 12 (claimed upper_bound)
witness operator (support, 12 qubits)
[22, 30, 32, 42, 49, 52, 61, 176, 177, 193, 194, 202]
certificate exact, d = 12 · scipy/HiGHS MILP
X: no logical < 12 exists; Z: no logical < 12 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 = 2.828
X checkZ checkqubit site (144)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 Liang, Zijian and Eberhardt, Jens Niklas and Chen, Yu-An
provenance literature baseline
construction Liang-Eberhardt-Chen [[288,8,12]] family, (12,12) lattice.
model classical construction (no AI model)
reference arXiv:2504.08887
date 2025-04-11
notes Reference baseline (Liang, Eberhardt, Chen).
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 140 · Z-checks 140
H_X (140 checks, sparse supports)
[0, 145, 146] [1, 146, 147] [2, 147, 148] [3, 148, 149] [4, 149, 150] [5, 150, 151] [6, 151, 152] [7, 152, 153] [8, 153, 154] [9, 154, 155] [0, 12, 157, 158] [1, 13, 158, 159] [2, 14, 159, 160] [3, 15, 160, 161] [4, 16, 161, 162] [5, 17, 162, 163] [6, 18, 163, 164] [7, 19, 164, 165] [8, 20, 165, 166] [9, 21, 166, 167] [2, 12, 24, 144, 169, 170] [3, 13, 25, 145, 170, 171] [4, 14, 26, 146, 171, 172] [5, 15, 27, 147, 172, 173] [6, 16, 28, 148, 173, 174] [7, 17, 29, 149, 174, 175] [8, 18, 30, 150, 175, 176] [9, 19, 31, 151, 176, 177] [10, 20, 32, 152, 177, 178] [11, 21, 33, 153, 178, 179] [14, 24, 36, 156, 181, 182] [15, 25, 37, 157, 182, 183] [16, 26, 38, 158, 183, 184] [17, 27, 39, 159, 184, 185] [18, 28, 40, 160, 185, 186] [19, 29, 41, 161, 186, 187] [20, 30, 42, 162, 187, 188] [21, 31, 43, 163, 188, 189] [22, 32, 44, 164, 189, 190] [23, 33, 45, 165, 190, 191] [26, 36, 48, 168, 193, 194] [27, 37, 49, 169, 194, 195] [28, 38, 50, 170, 195, 196] [29, 39, 51, 171, 196, 197] [30, 40, 52, 172, 197, 198] [31, 41, 53, 173, 198, 199] [32, 42, 54, 174, 199, 200] [33, 43, 55, 175, 200, 201] [34, 44, 56, 176, 201, 202] [35, 45, 57, 177, 202, 203] [38, 48, 60, 180, 205, 206] [39, 49, 61, 181, 206, 207] [40, 50, 62, 182, 207, 208] [41, 51, 63, 183, 208, 209] [42, 52, 64, 184, 209, 210] [43, 53, 65, 185, 210, 211] [44, 54, 66, 186, 211, 212] [45, 55, 67, 187, 212, 213] [46, 56, 68, 188, 213, 214] [47, 57, 69, 189, 214, 215] [50, 60, 72, 192, 217, 218] [51, 61, 73, 193, 218, 219] [52, 62, 74, 194, 219, 220] [53, 63, 75, 195, 220, 221] [54, 64, 76, 196, 221, 222] [55, 65, 77, 197, 222, 223] [56, 66, 78, 198, 223, 224] [57, 67, 79, 199, 224, 225] [58, 68, 80, 200, 225, 226] [59, 69, 81, 201, 226, 227] [62, 72, 84, 204, 229, 230] [63, 73, 85, 205, 230, 231] [64, 74, 86, 206, 231, 232] [65, 75, 87, 207, 232, 233] [66, 76, 88, 208, 233, 234] [67, 77, 89, 209, 234, 235] [68, 78, 90, 210, 235, 236] [69, 79, 91, 211, 236, 237] [70, 80, 92, 212, 237, 238] [71, 81, 93, 213, 238, 239] [74, 84, 96, 216, 241, 242] [75, 85, 97, 217, 242, 243] [76, 86, 98, 218, 243, 244] [77, 87, 99, 219, 244, 245] [78, 88, 100, 220, 245, 246] [79, 89, 101, 221, 246, 247] [80, 90, 102, 222, 247, 248] [81, 91, 103, 223, 248, 249] [82, 92, 104, 224, 249, 250] [83, 93, 105, 225, 250, 251] [86, 96, 108, 228, 253, 254] [87, 97, 109, 229, 254, 255] [88, 98, 110, 230, 255, 256] [89, 99, 111, 231, 256, 257] [90, 100, 112, 232, 257, 258] [91, 101, 113, 233, 258, 259] [92, 102, 114, 234, 259, 260] [93, 103, 115, 235, 260, 261] [94, 104, 116, 236, 261, 262] [95, 105, 117, 237, 262, 263] [98, 108, 120, 240, 265, 266] [99, 109, 121, 241, 266, 267] [100, 110, 122, 242, 267, 268] [101, 111, 123, 243, 268, 269] [102, 112, 124, 244, 269, 270] [103, 113, 125, 245, 270, 271] [104, 114, 126, 246, 271, 272] [105, 115, 127, 247, 272, 273] [106, 116, 128, 248, 273, 274] [107, 117, 129, 249, 274, 275] [110, 120, 132, 252, 277, 278] [111, 121, 133, 253, 278, 279] [112, 122, 134, 254, 279, 280] [113, 123, 135, 255, 280, 281] [114, 124, 136, 256, 281, 282] [115, 125, 137, 257, 282, 283] [116, 126, 138, 258, 283, 284] [117, 127, 139, 259, 284, 285] [118, 128, 140, 260, 285, 286] [119, 129, 141, 261, 286, 287] [122, 132, 264] [123, 133, 265] [124, 134, 266] [125, 135, 267] [126, 136, 268] [127, 137, 269] [128, 138, 270] [129, 139, 271] [130, 140, 272] [131, 141, 273] [134, 276] [135, 277] [136, 278] [137, 279] [138, 280] [139, 281] [140, 282] [141, 283] [142, 284] [143, 285]
H_Z (140 checks, sparse supports)
[24, 144, 156] [0, 25, 145, 157] [0, 1, 26, 146, 158, 168] [1, 2, 27, 147, 159, 169] [2, 3, 28, 148, 160, 170] [3, 4, 29, 149, 161, 171] [4, 5, 30, 150, 162, 172] [5, 6, 31, 151, 163, 173] [6, 7, 32, 152, 164, 174] [7, 8, 33, 153, 165, 175] [8, 9, 34, 154, 166, 176] [9, 10, 35, 155, 167, 177] [10, 11, 178] [11, 179] [36, 156, 168] [12, 37, 157, 169] [12, 13, 38, 158, 170, 180] [13, 14, 39, 159, 171, 181] [14, 15, 40, 160, 172, 182] [15, 16, 41, 161, 173, 183] [16, 17, 42, 162, 174, 184] [17, 18, 43, 163, 175, 185] [18, 19, 44, 164, 176, 186] [19, 20, 45, 165, 177, 187] [20, 21, 46, 166, 178, 188] [21, 22, 47, 167, 179, 189] [22, 23, 190] [23, 191] [48, 168, 180] [24, 49, 169, 181] [24, 25, 50, 170, 182, 192] [25, 26, 51, 171, 183, 193] [26, 27, 52, 172, 184, 194] [27, 28, 53, 173, 185, 195] [28, 29, 54, 174, 186, 196] [29, 30, 55, 175, 187, 197] [30, 31, 56, 176, 188, 198] [31, 32, 57, 177, 189, 199] [32, 33, 58, 178, 190, 200] [33, 34, 59, 179, 191, 201] [34, 35, 202] [35, 203] [60, 180, 192] [36, 61, 181, 193] [36, 37, 62, 182, 194, 204] [37, 38, 63, 183, 195, 205] [38, 39, 64, 184, 196, 206] [39, 40, 65, 185, 197, 207] [40, 41, 66, 186, 198, 208] [41, 42, 67, 187, 199, 209] [42, 43, 68, 188, 200, 210] [43, 44, 69, 189, 201, 211] [44, 45, 70, 190, 202, 212] [45, 46, 71, 191, 203, 213] [46, 47, 214] [47, 215] [72, 192, 204] [48, 73, 193, 205] [48, 49, 74, 194, 206, 216] [49, 50, 75, 195, 207, 217] [50, 51, 76, 196, 208, 218] [51, 52, 77, 197, 209, 219] [52, 53, 78, 198, 210, 220] [53, 54, 79, 199, 211, 221] [54, 55, 80, 200, 212, 222] [55, 56, 81, 201, 213, 223] [56, 57, 82, 202, 214, 224] [57, 58, 83, 203, 215, 225] [58, 59, 226] [59, 227] [84, 204, 216] [60, 85, 205, 217] [60, 61, 86, 206, 218, 228] [61, 62, 87, 207, 219, 229] [62, 63, 88, 208, 220, 230] [63, 64, 89, 209, 221, 231] [64, 65, 90, 210, 222, 232] [65, 66, 91, 211, 223, 233] [66, 67, 92, 212, 224, 234] [67, 68, 93, 213, 225, 235] [68, 69, 94, 214, 226, 236] [69, 70, 95, 215, 227, 237] [70, 71, 238] [71, 239] [96, 216, 228] [72, 97, 217, 229] [72, 73, 98, 218, 230, 240] [73, 74, 99, 219, 231, 241] [74, 75, 100, 220, 232, 242] [75, 76, 101, 221, 233, 243] [76, 77, 102, 222, 234, 244] [77, 78, 103, 223, 235, 245] [78, 79, 104, 224, 236, 246] [79, 80, 105, 225, 237, 247] [80, 81, 106, 226, 238, 248] [81, 82, 107, 227, 239, 249] [82, 83, 250] [83, 251] [108, 228, 240] [84, 109, 229, 241] [84, 85, 110, 230, 242, 252] [85, 86, 111, 231, 243, 253] [86, 87, 112, 232, 244, 254] [87, 88, 113, 233, 245, 255] [88, 89, 114, 234, 246, 256] [89, 90, 115, 235, 247, 257] [90, 91, 116, 236, 248, 258] [91, 92, 117, 237, 249, 259] [92, 93, 118, 238, 250, 260] [93, 94, 119, 239, 251, 261] [94, 95, 262] [95, 263] [120, 240, 252] [96, 121, 241, 253] [96, 97, 122, 242, 254, 264] [97, 98, 123, 243, 255, 265] [98, 99, 124, 244, 256, 266] [99, 100, 125, 245, 257, 267] [100, 101, 126, 246, 258, 268] [101, 102, 127, 247, 259, 269] [102, 103, 128, 248, 260, 270] [103, 104, 129, 249, 261, 271] [104, 105, 130, 250, 262, 272] [105, 106, 131, 251, 263, 273] [106, 107, 274] [107, 275] [132, 252, 264] [108, 133, 253, 265] [108, 109, 134, 254, 266, 276] [109, 110, 135, 255, 267, 277] [110, 111, 136, 256, 268, 278] [111, 112, 137, 257, 269, 279] [112, 113, 138, 258, 270, 280] [113, 114, 139, 259, 271, 281] [114, 115, 140, 260, 272, 282] [115, 116, 141, 261, 273, 283] [116, 117, 142, 262, 274, 284] [117, 118, 143, 263, 275, 285] [118, 119, 286] [119, 287]
raw submission JSON