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[[294,12,14]] d ≤
n
294
k
12
d
14
kd²/n
8.0
w
8
g
0.004
r
6.7082
layers
2

Share this result

Distance

d_X 14 · witness weight 14 (claimed upper_bound)
witness operator (support, 14 qubits)
[10, 11, 52, 69, 91, 170, 187, 207, 226, 245, 263, 266, 268, 286]
d_Z 14 · witness weight 14 (claimed upper_bound)
witness operator (support, 14 qubits)
[43, 48, 53, 61, 71, 81, 91, 94, 98, 137, 138, 176, 231, 248]
certificate none yet · distance stands as a self-certified upper bound (d ≤)

Verified 2D layout

as measured by the verifier: every check drawn over the submitted coordinates; the interaction radius is the longest dashed pair
r = 6.708
X checkZ checkqubit site (178)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 @vprusso
provenance submitted through the challenge
novelty new parameter set claimed by submitter
construction Weight-8 planar open-boundary bivariate-bicycle code (tile-code family) from the boundary engine; f=[(0, 0), (1, 0), (2, 3), (2, -2)], g=[(0, 0), (0, 1), (-1, -1), (-1, 3)] on a 9x20 lattice.
model Claude Claude Opus 4.8 (claimed, not verified)
builds on arXiv:2504.09171, arXiv:2606.19482, arXiv:2504.08887
date 2026-06-25
notes Novelty audit (2026-07-01): the exact [[294,12,14]] triple appears in none of the checked sources (tile codes arXiv:2504.09171; planar BB arXiv:2504.08887; twisted-tori arXiv:2503.03827; nearest-neighbour planar arXiv:2606.19482; bracket-string web search), so the parameter set is new. It is, however, strictly dominated by the weight-8 planar open-boundary [[282,12,14]] published in arXiv:2504.08887 (v3+, stated in the abstract): same k, d, and weight at smaller n, in the same 2D-local planar class. Any frontier position here is board-local; a faithful seed of [[282,12,14]] would displace this code, but is not currently possible: the paper specifies its boundary stabilizers (including non-truncation secondary gauge operators) and the 10 grafted-away qubits only in figures (Figs. 7 and 28), with no machine-readable data published. It is cited as a reference bar in TRACKS.md instead.
family tile (a tag, not a ranking)
locality 2D-local bilayer (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 183 · Z-checks 172
H_X (183 checks, sparse supports)
[2, 20, 25, 140, 144, 160, 161] [3, 21, 26, 141, 145, 161, 162] [4, 22, 27, 142, 146, 162, 163] [5, 23, 28, 143, 147, 163, 164] [6, 24, 29, 144, 148, 164, 165] [7, 25, 30, 145, 149, 165, 166] [8, 26, 31, 146, 150, 166, 167] [9, 27, 32, 147, 151, 167, 168] [10, 28, 33, 148, 152, 168, 169] [11, 29, 34, 149, 153, 169, 170] [12, 30, 35, 150, 154, 170, 171] [13, 31, 36, 151, 155, 171, 172] [14, 32, 37, 152, 156, 172, 173] [15, 33, 38, 153, 157, 173, 174] [16, 34, 39, 154, 158, 174, 175] [2, 22, 40, 45, 159, 163, 179, 180] [3, 23, 41, 46, 160, 164, 180, 181] [4, 24, 42, 47, 161, 165, 181, 182] [5, 25, 43, 48, 162, 166, 182, 183] [6, 26, 44, 49, 163, 167, 183, 184] [7, 27, 45, 50, 164, 168, 184, 185] [8, 28, 46, 51, 165, 169, 185, 186] [9, 29, 47, 52, 166, 170, 186, 187] [10, 30, 48, 53, 167, 171, 187, 188] [11, 31, 49, 54, 168, 172, 188, 189] [12, 32, 50, 55, 169, 173, 189, 190] [13, 33, 51, 56, 170, 174, 190, 191] [14, 34, 52, 57, 171, 175, 191, 192] [15, 35, 53, 58, 172, 176, 192, 193] [16, 36, 54, 59, 173, 177, 193, 194] [22, 42, 60, 65, 178, 182, 198, 199] [23, 43, 61, 66, 179, 183, 199, 200] [24, 44, 62, 67, 180, 184, 200, 201] [25, 45, 63, 68, 181, 185, 201, 202] [26, 46, 64, 69, 182, 186, 202, 203] [27, 47, 65, 70, 183, 187, 203, 204] [28, 48, 66, 71, 184, 188, 204, 205] [29, 49, 67, 72, 185, 189, 205, 206] [30, 50, 68, 73, 186, 190, 206, 207] [31, 51, 69, 74, 187, 191, 207, 208] [32, 52, 70, 75, 188, 192, 208, 209] [33, 53, 71, 76, 189, 193, 209, 210] [34, 54, 72, 77, 190, 194, 210, 211] [35, 55, 73, 78, 191, 195, 211, 212] [36, 56, 74, 79, 192, 196, 212, 213] [42, 62, 80, 85, 197, 201, 217, 218] [43, 63, 81, 86, 198, 202, 218, 219] [44, 64, 82, 87, 199, 203, 219, 220] [45, 65, 83, 88, 200, 204, 220, 221] [46, 66, 84, 89, 201, 205, 221, 222] [47, 67, 85, 90, 202, 206, 222, 223] [48, 68, 86, 91, 203, 207, 223, 224] [49, 69, 87, 92, 204, 208, 224, 225] [50, 70, 88, 93, 205, 209, 225, 226] [51, 71, 89, 94, 206, 210, 226, 227] [52, 72, 90, 95, 207, 211, 227, 228] [53, 73, 91, 96, 208, 212, 228, 229] [54, 74, 92, 97, 209, 213, 229, 230] [55, 75, 93, 98, 210, 214, 230, 231] [56, 76, 94, 99, 211, 215, 231, 232] [62, 82, 100, 105, 216, 220, 236, 237] [63, 83, 101, 106, 217, 221, 237, 238] [64, 84, 102, 107, 218, 222, 238, 239] [65, 85, 103, 108, 219, 223, 239, 240] [66, 86, 104, 109, 220, 224, 240, 241] [67, 87, 105, 110, 221, 225, 241, 242] [68, 88, 106, 111, 222, 226, 242, 243] [69, 89, 107, 112, 223, 227, 243, 244] [70, 90, 108, 113, 224, 228, 244, 245] [71, 91, 109, 114, 225, 229, 245, 246] [72, 92, 110, 115, 226, 230, 246, 247] [73, 93, 111, 116, 227, 231, 247, 248] [74, 94, 112, 117, 228, 232, 248, 249] [75, 95, 113, 118, 229, 233, 249, 250] [76, 96, 114, 119, 230, 234, 250, 251] [82, 102, 120, 125, 235, 239, 256, 257] [83, 103, 121, 126, 236, 240, 257, 258] [84, 104, 122, 127, 237, 241, 258, 259] [85, 105, 123, 128, 238, 242, 259, 260] [86, 106, 124, 129, 239, 243, 260, 261] [87, 107, 125, 130, 240, 244, 261, 262] [88, 108, 126, 131, 241, 245, 262, 263] [89, 109, 127, 132, 242, 246, 263, 264] [90, 110, 128, 133, 243, 247, 264, 265] [91, 111, 129, 134, 244, 248, 265, 266] [92, 112, 130, 135, 245, 249, 266, 267] [93, 113, 131, 136, 246, 250, 267, 268] [94, 114, 132, 137, 247, 251, 268, 269] [95, 115, 133, 138, 248, 252, 269, 270] [96, 116, 134, 139, 249, 253, 270, 271] [0, 1, 2, 3, 4, 141] [1, 2, 3, 4, 5, 142] [2, 3, 4, 5, 6, 143] [3, 4, 5, 6, 7, 144] [4, 5, 6, 7, 8, 145] [5, 6, 7, 8, 9, 146] [6, 7, 8, 9, 10, 147] [7, 8, 9, 10, 11, 148] [8, 9, 10, 11, 12, 149] [9, 10, 11, 12, 13, 150] [10, 11, 12, 13, 14, 151] [11, 12, 13, 14, 15, 152] [12, 13, 14, 15, 16, 153] [13, 14, 15, 16, 17, 154] [14, 15, 16, 17, 18, 155] [15, 16, 17, 18, 19, 156] [2, 20, 25, 140, 144, 160, 161] [3, 21, 26, 141, 145, 161, 162] [4, 22, 27, 142, 146, 162, 163] [5, 23, 28, 143, 147, 163, 164] [6, 24, 29, 144, 148, 164, 165] [7, 25, 30, 145, 149, 165, 166] [8, 26, 31, 146, 150, 166, 167] [9, 27, 32, 147, 151, 167, 168] [10, 28, 33, 148, 152, 168, 169] [11, 29, 34, 149, 153, 169, 170] [12, 30, 35, 150, 154, 170, 171] [13, 31, 36, 151, 155, 171, 172] [14, 32, 37, 152, 156, 172, 173] [15, 33, 38, 153, 157, 173, 174] [16, 34, 39, 154, 158, 174, 175] [0, 5, 141, 142] [1, 6, 142, 143] [2, 7, 143, 144] [3, 8, 144, 145] [4, 9, 145, 146] [5, 10, 146, 147] [6, 11, 147, 148] [7, 12, 148, 149] [8, 13, 149, 150] [9, 14, 150, 151] [10, 15, 151, 152] [11, 16, 152, 153] [12, 17, 153, 154] [13, 18, 154, 155] [14, 19, 155, 156] [122, 275, 279] [123, 276, 280] [124, 277, 281] [125, 278, 282] [126, 279, 283] [127, 280, 284] [128, 281, 285] [129, 282, 286] [130, 283, 287] [131, 284, 288] [132, 285, 289] [133, 286, 290] [134, 287, 291] [135, 288, 292] [136, 289, 293] [102, 122, 255, 259, 276, 277] [103, 123, 256, 260, 277, 278] [104, 124, 257, 261, 278, 279] [105, 125, 258, 262, 279, 280] [106, 126, 259, 263, 280, 281] [107, 127, 260, 264, 281, 282] [108, 128, 261, 265, 282, 283] [109, 129, 262, 266, 283, 284] [110, 130, 263, 267, 284, 285] [111, 131, 264, 268, 285, 286] [112, 132, 265, 269, 286, 287] [113, 133, 266, 270, 287, 288] [114, 134, 267, 271, 288, 289] [115, 135, 268, 272, 289, 290] [116, 136, 269, 273, 290, 291] [122, 275, 279] [123, 276, 280] [124, 277, 281] [125, 278, 282] [126, 279, 283] [127, 280, 284] [128, 281, 285] [129, 282, 286] [130, 283, 287] [131, 284, 288] [132, 285, 289] [133, 286, 290] [134, 287, 291] [135, 288, 292] [136, 289, 293] [101, 121, 254, 258, 275, 276] [121, 274, 278]
H_Z (172 checks, sparse supports)
[2, 3, 20, 24, 144, 161, 180] [3, 4, 21, 25, 140, 145, 162, 181] [4, 5, 22, 26, 141, 146, 163, 182] [5, 6, 23, 27, 142, 147, 164, 183] [6, 7, 24, 28, 143, 148, 165, 184] [7, 8, 25, 29, 144, 149, 166, 185] [8, 9, 26, 30, 145, 150, 167, 186] [9, 10, 27, 31, 146, 151, 168, 187] [10, 11, 28, 32, 147, 152, 169, 188] [11, 12, 29, 33, 148, 153, 170, 189] [12, 13, 30, 34, 149, 154, 171, 190] [13, 14, 31, 35, 150, 155, 172, 191] [14, 15, 32, 36, 151, 156, 173, 192] [15, 16, 33, 37, 152, 157, 174, 193] [16, 17, 34, 38, 153, 158, 175, 194] [22, 23, 40, 44, 163, 180, 199] [23, 24, 41, 45, 159, 164, 181, 200] [24, 25, 42, 46, 160, 165, 182, 201] [25, 26, 43, 47, 161, 166, 183, 202] [26, 27, 44, 48, 162, 167, 184, 203] [27, 28, 45, 49, 163, 168, 185, 204] [28, 29, 46, 50, 164, 169, 186, 205] [29, 30, 47, 51, 165, 170, 187, 206] [30, 31, 48, 52, 166, 171, 188, 207] [31, 32, 49, 53, 167, 172, 189, 208] [32, 33, 50, 54, 168, 173, 190, 209] [33, 34, 51, 55, 169, 174, 191, 210] [34, 35, 52, 56, 170, 175, 192, 211] [35, 36, 53, 57, 171, 176, 193, 212] [36, 37, 54, 58, 172, 177, 194, 213] [42, 43, 60, 64, 182, 199, 218] [43, 44, 61, 65, 178, 183, 200, 219] [44, 45, 62, 66, 179, 184, 201, 220] [45, 46, 63, 67, 180, 185, 202, 221] [46, 47, 64, 68, 181, 186, 203, 222] [47, 48, 65, 69, 182, 187, 204, 223] [48, 49, 66, 70, 183, 188, 205, 224] [49, 50, 67, 71, 184, 189, 206, 225] [50, 51, 68, 72, 185, 190, 207, 226] [51, 52, 69, 73, 186, 191, 208, 227] [52, 53, 70, 74, 187, 192, 209, 228] [53, 54, 71, 75, 188, 193, 210, 229] [54, 55, 72, 76, 189, 194, 211, 230] [55, 56, 73, 77, 190, 195, 212, 231] [56, 57, 74, 78, 191, 196, 213, 232] [62, 63, 80, 84, 201, 218, 237] [63, 64, 81, 85, 197, 202, 219, 238] [64, 65, 82, 86, 198, 203, 220, 239] [65, 66, 83, 87, 199, 204, 221, 240] [66, 67, 84, 88, 200, 205, 222, 241] [67, 68, 85, 89, 201, 206, 223, 242] [68, 69, 86, 90, 202, 207, 224, 243] [69, 70, 87, 91, 203, 208, 225, 244] [70, 71, 88, 92, 204, 209, 226, 245] [71, 72, 89, 93, 205, 210, 227, 246] [72, 73, 90, 94, 206, 211, 228, 247] [73, 74, 91, 95, 207, 212, 229, 248] [74, 75, 92, 96, 208, 213, 230, 249] [75, 76, 93, 97, 209, 214, 231, 250] [76, 77, 94, 98, 210, 215, 232, 251] [82, 83, 100, 104, 220, 237, 257] [83, 84, 101, 105, 216, 221, 238, 258] [84, 85, 102, 106, 217, 222, 239, 259] [85, 86, 103, 107, 218, 223, 240, 260] [86, 87, 104, 108, 219, 224, 241, 261] [87, 88, 105, 109, 220, 225, 242, 262] [88, 89, 106, 110, 221, 226, 243, 263] [89, 90, 107, 111, 222, 227, 244, 264] [90, 91, 108, 112, 223, 228, 245, 265] [91, 92, 109, 113, 224, 229, 246, 266] [92, 93, 110, 114, 225, 230, 247, 267] [93, 94, 111, 115, 226, 231, 248, 268] [94, 95, 112, 116, 227, 232, 249, 269] [95, 96, 113, 117, 228, 233, 250, 270] [96, 97, 114, 118, 229, 234, 251, 271] [102, 103, 120, 124, 239, 257, 277] [103, 104, 121, 125, 235, 240, 258, 278] [104, 105, 122, 126, 236, 241, 259, 279] [105, 106, 123, 127, 237, 242, 260, 280] [106, 107, 124, 128, 238, 243, 261, 281] [107, 108, 125, 129, 239, 244, 262, 282] [108, 109, 126, 130, 240, 245, 263, 283] [109, 110, 127, 131, 241, 246, 264, 284] [110, 111, 128, 132, 242, 247, 265, 285] [111, 112, 129, 133, 243, 248, 266, 286] [112, 113, 130, 134, 244, 249, 267, 287] [113, 114, 131, 135, 245, 250, 268, 288] [114, 115, 132, 136, 246, 251, 269, 289] [115, 116, 133, 137, 247, 252, 270, 290] [116, 117, 134, 138, 248, 253, 271, 291] [20, 140] [40, 159] [60, 178] [80, 197] [100, 216] [120, 235] [0, 21, 141] [20, 41, 160] [40, 61, 179] [60, 81, 198] [0, 1, 22, 142, 159, 178] [20, 21, 42, 161, 178, 197] [40, 41, 62, 180, 197, 216] [60, 61, 82, 199, 216, 235] [80, 81, 102, 218, 235, 255] [100, 101, 122, 237, 255, 275] [1, 2, 23, 143, 160, 179] [21, 22, 43, 162, 179, 198] [41, 42, 63, 181, 198, 217] [61, 62, 83, 200, 217, 236] [81, 82, 103, 219, 236, 256] [101, 102, 123, 238, 256, 276] [2, 3, 20, 24, 144, 161, 180] [22, 23, 40, 44, 163, 180, 199] [42, 43, 60, 64, 182, 199, 218] [62, 63, 80, 84, 201, 218, 237] [82, 83, 100, 104, 220, 237, 257] [102, 103, 120, 124, 239, 257, 277] [3, 4, 20, 21, 25, 145, 162, 181] [23, 24, 40, 41, 45, 164, 181, 200] [43, 44, 60, 61, 65, 183, 200, 219] [63, 64, 80, 81, 85, 202, 219, 238] [83, 84, 100, 101, 105, 221, 238, 258] [103, 104, 120, 121, 125, 240, 258, 278] [0, 21, 141] [20, 41, 160] [40, 61, 179] [60, 81, 198] [80, 101, 217, 254] [100, 121, 236, 254, 274] [39, 158] [59, 177] [79, 196] [99, 215] [119, 234] [139, 253] [38, 157] [58, 176] [78, 195] [98, 214] [118, 233] [138, 252] [19, 37, 156] [39, 57, 175] [59, 77, 194] [79, 97, 213] [99, 117, 232] [119, 137, 251] [18, 19, 36, 155, 177, 196] [38, 39, 56, 174, 196, 215] [58, 59, 76, 193, 215, 234] [78, 79, 96, 212, 234, 253] [98, 99, 116, 231, 253, 273] [118, 119, 136, 250, 273, 293] [17, 18, 35, 39, 154, 176, 195] [37, 38, 55, 59, 173, 195, 214] [57, 58, 75, 79, 192, 214, 233] [77, 78, 95, 99, 211, 233, 252] [97, 98, 115, 119, 230, 252, 272] [117, 118, 135, 139, 249, 272, 292] [16, 17, 34, 38, 39, 153, 175, 194] [36, 37, 54, 58, 59, 172, 194, 213] [56, 57, 74, 78, 79, 191, 213, 232] [76, 77, 94, 98, 99, 210, 232, 251] [96, 97, 114, 118, 119, 229, 251, 271] [116, 117, 134, 138, 139, 248, 271, 291] [15, 16, 33, 37, 38, 152, 174, 193] [35, 36, 53, 57, 58, 171, 193, 212] [55, 56, 73, 77, 78, 190, 212, 231] [75, 76, 93, 97, 98, 209, 231, 250] [95, 96, 113, 117, 118, 228, 250, 270] [115, 116, 133, 137, 138, 247, 270, 290]
raw submission JSON