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[[392,8,15]] d ≤
n
392
k
8
d
15
kd²/n
4.592
w
6
g
0.0717
r
2.8284
layers
2

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Distance

d_X 15 · witness weight 15 (claimed upper_bound)
witness operator (support, 15 qubits)
[45, 74, 75, 103, 105, 132, 133, 134, 147, 177, 199, 213, 329, 358, 384]
d_Z 15 · witness weight 15 (claimed upper_bound)
witness operator (support, 15 qubits)
[68, 94, 108, 120, 122, 124, 136, 146, 148, 160, 169, 172, 183, 365, 366]
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 = 2.828
X checkZ checkqubit site (196)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 @mathysrennela
provenance submitted through the challenge
novelty known parameter set; see provenance notes
construction Open-boundary planar bivariate-bicycle (Liang-Eberhardt-Chen / Liang-Yang-Iosue-Chen, arXiv:2504.08887) on a 14x14 grid; f = x + x2 + y2, g = 1 + x2 y + x2 y2; built with the directional anyon-condensation truncation, corner-resolved, bilayer layout.
model Tencent Hy3 (claimed, not verified)
builds on arXiv:2504.08887, arXiv:2410.11942
date 2026-07-15
notes LITERATURE NOVELTY: NOT NOVEL. This is the L=14 member of the flagship planar BB family f=x+x^2+y^2, g=1+x^2 y+x^2 y^2 from Liang, Eberhardt & Chen, 'Planar quantum LDPC codes with open boundaries' (arXiv:2504.08887), Eq. 9 / Table V. The paper already publishes this exact (f,g) family at L=6,8,10,12 ([[72,8,4]],[[128,8,6]],[[200,8,9]],[[288,8,12]]); [[392,8,15]] is a mechanical lattice-size extension, not a new construction. It is also the same family as the board's own local-2d-bilayer weight-6 bar-holder [[288,8,12]] (L=12). Board status: passes the trusted gate (passed=true), advances the local-2d-bilayer weight-6 cell (kd^2/n=4.59 vs 4.00 bar), but is NOT a literature discovery. Distance is an upper_bound witness, not server-certified exact.
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 192 · Z-checks 192
H_X (192 checks, sparse supports)
[0, 197, 198] [1, 198, 199] [2, 199, 200] [3, 200, 201] [4, 201, 202] [5, 202, 203] [6, 203, 204] [7, 204, 205] [8, 205, 206] [9, 206, 207] [10, 207, 208] [11, 208, 209] [0, 14, 211, 212] [1, 15, 212, 213] [2, 16, 213, 214] [3, 17, 214, 215] [4, 18, 215, 216] [5, 19, 216, 217] [6, 20, 217, 218] [7, 21, 218, 219] [8, 22, 219, 220] [9, 23, 220, 221] [10, 24, 221, 222] [11, 25, 222, 223] [2, 14, 28, 196, 225, 226] [3, 15, 29, 197, 226, 227] [4, 16, 30, 198, 227, 228] [5, 17, 31, 199, 228, 229] [6, 18, 32, 200, 229, 230] [7, 19, 33, 201, 230, 231] [8, 20, 34, 202, 231, 232] [9, 21, 35, 203, 232, 233] [10, 22, 36, 204, 233, 234] [11, 23, 37, 205, 234, 235] [12, 24, 38, 206, 235, 236] [13, 25, 39, 207, 236, 237] [16, 28, 42, 210, 239, 240] [17, 29, 43, 211, 240, 241] [18, 30, 44, 212, 241, 242] [19, 31, 45, 213, 242, 243] [20, 32, 46, 214, 243, 244] [21, 33, 47, 215, 244, 245] [22, 34, 48, 216, 245, 246] [23, 35, 49, 217, 246, 247] [24, 36, 50, 218, 247, 248] [25, 37, 51, 219, 248, 249] [26, 38, 52, 220, 249, 250] [27, 39, 53, 221, 250, 251] [30, 42, 56, 224, 253, 254] [31, 43, 57, 225, 254, 255] [32, 44, 58, 226, 255, 256] [33, 45, 59, 227, 256, 257] [34, 46, 60, 228, 257, 258] [35, 47, 61, 229, 258, 259] [36, 48, 62, 230, 259, 260] [37, 49, 63, 231, 260, 261] [38, 50, 64, 232, 261, 262] [39, 51, 65, 233, 262, 263] [40, 52, 66, 234, 263, 264] [41, 53, 67, 235, 264, 265] [44, 56, 70, 238, 267, 268] [45, 57, 71, 239, 268, 269] [46, 58, 72, 240, 269, 270] [47, 59, 73, 241, 270, 271] [48, 60, 74, 242, 271, 272] [49, 61, 75, 243, 272, 273] [50, 62, 76, 244, 273, 274] [51, 63, 77, 245, 274, 275] [52, 64, 78, 246, 275, 276] [53, 65, 79, 247, 276, 277] [54, 66, 80, 248, 277, 278] [55, 67, 81, 249, 278, 279] [58, 70, 84, 252, 281, 282] [59, 71, 85, 253, 282, 283] [60, 72, 86, 254, 283, 284] [61, 73, 87, 255, 284, 285] [62, 74, 88, 256, 285, 286] [63, 75, 89, 257, 286, 287] [64, 76, 90, 258, 287, 288] [65, 77, 91, 259, 288, 289] [66, 78, 92, 260, 289, 290] [67, 79, 93, 261, 290, 291] [68, 80, 94, 262, 291, 292] [69, 81, 95, 263, 292, 293] [72, 84, 98, 266, 295, 296] [73, 85, 99, 267, 296, 297] [74, 86, 100, 268, 297, 298] [75, 87, 101, 269, 298, 299] [76, 88, 102, 270, 299, 300] [77, 89, 103, 271, 300, 301] [78, 90, 104, 272, 301, 302] [79, 91, 105, 273, 302, 303] [80, 92, 106, 274, 303, 304] [81, 93, 107, 275, 304, 305] [82, 94, 108, 276, 305, 306] [83, 95, 109, 277, 306, 307] [86, 98, 112, 280, 309, 310] [87, 99, 113, 281, 310, 311] [88, 100, 114, 282, 311, 312] [89, 101, 115, 283, 312, 313] [90, 102, 116, 284, 313, 314] [91, 103, 117, 285, 314, 315] [92, 104, 118, 286, 315, 316] [93, 105, 119, 287, 316, 317] [94, 106, 120, 288, 317, 318] [95, 107, 121, 289, 318, 319] [96, 108, 122, 290, 319, 320] [97, 109, 123, 291, 320, 321] [100, 112, 126, 294, 323, 324] [101, 113, 127, 295, 324, 325] [102, 114, 128, 296, 325, 326] [103, 115, 129, 297, 326, 327] [104, 116, 130, 298, 327, 328] [105, 117, 131, 299, 328, 329] [106, 118, 132, 300, 329, 330] [107, 119, 133, 301, 330, 331] [108, 120, 134, 302, 331, 332] [109, 121, 135, 303, 332, 333] [110, 122, 136, 304, 333, 334] [111, 123, 137, 305, 334, 335] [114, 126, 140, 308, 337, 338] [115, 127, 141, 309, 338, 339] [116, 128, 142, 310, 339, 340] [117, 129, 143, 311, 340, 341] [118, 130, 144, 312, 341, 342] [119, 131, 145, 313, 342, 343] [120, 132, 146, 314, 343, 344] [121, 133, 147, 315, 344, 345] [122, 134, 148, 316, 345, 346] [123, 135, 149, 317, 346, 347] [124, 136, 150, 318, 347, 348] [125, 137, 151, 319, 348, 349] [128, 140, 154, 322, 351, 352] [129, 141, 155, 323, 352, 353] [130, 142, 156, 324, 353, 354] [131, 143, 157, 325, 354, 355] [132, 144, 158, 326, 355, 356] [133, 145, 159, 327, 356, 357] [134, 146, 160, 328, 357, 358] [135, 147, 161, 329, 358, 359] [136, 148, 162, 330, 359, 360] [137, 149, 163, 331, 360, 361] [138, 150, 164, 332, 361, 362] [139, 151, 165, 333, 362, 363] [142, 154, 168, 336, 365, 366] [143, 155, 169, 337, 366, 367] [144, 156, 170, 338, 367, 368] [145, 157, 171, 339, 368, 369] [146, 158, 172, 340, 369, 370] [147, 159, 173, 341, 370, 371] [148, 160, 174, 342, 371, 372] [149, 161, 175, 343, 372, 373] [150, 162, 176, 344, 373, 374] [151, 163, 177, 345, 374, 375] [152, 164, 178, 346, 375, 376] [153, 165, 179, 347, 376, 377] [156, 168, 182, 350, 379, 380] [157, 169, 183, 351, 380, 381] [158, 170, 184, 352, 381, 382] [159, 171, 185, 353, 382, 383] [160, 172, 186, 354, 383, 384] [161, 173, 187, 355, 384, 385] [162, 174, 188, 356, 385, 386] [163, 175, 189, 357, 386, 387] [164, 176, 190, 358, 387, 388] [165, 177, 191, 359, 388, 389] [166, 178, 192, 360, 389, 390] [167, 179, 193, 361, 390, 391] [170, 182, 364] [171, 183, 365] [172, 184, 366] [173, 185, 367] [174, 186, 368] [175, 187, 369] [176, 188, 370] [177, 189, 371] [178, 190, 372] [179, 191, 373] [180, 192, 374] [181, 193, 375] [184, 378] [185, 379] [186, 380] [187, 381] [188, 382] [189, 383] [190, 384] [191, 385] [192, 386] [193, 387] [194, 388] [195, 389]
H_Z (192 checks, sparse supports)
[28, 196, 210] [0, 29, 197, 211] [0, 1, 30, 198, 212, 224] [1, 2, 31, 199, 213, 225] [2, 3, 32, 200, 214, 226] [3, 4, 33, 201, 215, 227] [4, 5, 34, 202, 216, 228] [5, 6, 35, 203, 217, 229] [6, 7, 36, 204, 218, 230] [7, 8, 37, 205, 219, 231] [8, 9, 38, 206, 220, 232] [9, 10, 39, 207, 221, 233] [10, 11, 40, 208, 222, 234] [11, 12, 41, 209, 223, 235] [12, 13, 236] [13, 237] [42, 210, 224] [14, 43, 211, 225] [14, 15, 44, 212, 226, 238] [15, 16, 45, 213, 227, 239] [16, 17, 46, 214, 228, 240] [17, 18, 47, 215, 229, 241] [18, 19, 48, 216, 230, 242] [19, 20, 49, 217, 231, 243] [20, 21, 50, 218, 232, 244] [21, 22, 51, 219, 233, 245] [22, 23, 52, 220, 234, 246] [23, 24, 53, 221, 235, 247] [24, 25, 54, 222, 236, 248] [25, 26, 55, 223, 237, 249] [26, 27, 250] [27, 251] [56, 224, 238] [28, 57, 225, 239] [28, 29, 58, 226, 240, 252] [29, 30, 59, 227, 241, 253] [30, 31, 60, 228, 242, 254] [31, 32, 61, 229, 243, 255] [32, 33, 62, 230, 244, 256] [33, 34, 63, 231, 245, 257] [34, 35, 64, 232, 246, 258] [35, 36, 65, 233, 247, 259] [36, 37, 66, 234, 248, 260] [37, 38, 67, 235, 249, 261] [38, 39, 68, 236, 250, 262] [39, 40, 69, 237, 251, 263] [40, 41, 264] [41, 265] [70, 238, 252] [42, 71, 239, 253] [42, 43, 72, 240, 254, 266] [43, 44, 73, 241, 255, 267] [44, 45, 74, 242, 256, 268] [45, 46, 75, 243, 257, 269] [46, 47, 76, 244, 258, 270] [47, 48, 77, 245, 259, 271] [48, 49, 78, 246, 260, 272] [49, 50, 79, 247, 261, 273] [50, 51, 80, 248, 262, 274] [51, 52, 81, 249, 263, 275] [52, 53, 82, 250, 264, 276] [53, 54, 83, 251, 265, 277] [54, 55, 278] [55, 279] [84, 252, 266] [56, 85, 253, 267] [56, 57, 86, 254, 268, 280] [57, 58, 87, 255, 269, 281] [58, 59, 88, 256, 270, 282] [59, 60, 89, 257, 271, 283] [60, 61, 90, 258, 272, 284] [61, 62, 91, 259, 273, 285] [62, 63, 92, 260, 274, 286] [63, 64, 93, 261, 275, 287] [64, 65, 94, 262, 276, 288] [65, 66, 95, 263, 277, 289] [66, 67, 96, 264, 278, 290] [67, 68, 97, 265, 279, 291] [68, 69, 292] [69, 293] [98, 266, 280] [70, 99, 267, 281] [70, 71, 100, 268, 282, 294] [71, 72, 101, 269, 283, 295] [72, 73, 102, 270, 284, 296] [73, 74, 103, 271, 285, 297] [74, 75, 104, 272, 286, 298] [75, 76, 105, 273, 287, 299] [76, 77, 106, 274, 288, 300] [77, 78, 107, 275, 289, 301] [78, 79, 108, 276, 290, 302] [79, 80, 109, 277, 291, 303] [80, 81, 110, 278, 292, 304] [81, 82, 111, 279, 293, 305] [82, 83, 306] [83, 307] [112, 280, 294] [84, 113, 281, 295] [84, 85, 114, 282, 296, 308] [85, 86, 115, 283, 297, 309] [86, 87, 116, 284, 298, 310] [87, 88, 117, 285, 299, 311] [88, 89, 118, 286, 300, 312] [89, 90, 119, 287, 301, 313] [90, 91, 120, 288, 302, 314] [91, 92, 121, 289, 303, 315] [92, 93, 122, 290, 304, 316] [93, 94, 123, 291, 305, 317] [94, 95, 124, 292, 306, 318] [95, 96, 125, 293, 307, 319] [96, 97, 320] [97, 321] [126, 294, 308] [98, 127, 295, 309] [98, 99, 128, 296, 310, 322] [99, 100, 129, 297, 311, 323] [100, 101, 130, 298, 312, 324] [101, 102, 131, 299, 313, 325] [102, 103, 132, 300, 314, 326] [103, 104, 133, 301, 315, 327] [104, 105, 134, 302, 316, 328] [105, 106, 135, 303, 317, 329] [106, 107, 136, 304, 318, 330] [107, 108, 137, 305, 319, 331] [108, 109, 138, 306, 320, 332] [109, 110, 139, 307, 321, 333] [110, 111, 334] [111, 335] [140, 308, 322] [112, 141, 309, 323] [112, 113, 142, 310, 324, 336] [113, 114, 143, 311, 325, 337] [114, 115, 144, 312, 326, 338] [115, 116, 145, 313, 327, 339] [116, 117, 146, 314, 328, 340] [117, 118, 147, 315, 329, 341] [118, 119, 148, 316, 330, 342] [119, 120, 149, 317, 331, 343] [120, 121, 150, 318, 332, 344] [121, 122, 151, 319, 333, 345] [122, 123, 152, 320, 334, 346] [123, 124, 153, 321, 335, 347] [124, 125, 348] [125, 349] [154, 322, 336] [126, 155, 323, 337] [126, 127, 156, 324, 338, 350] [127, 128, 157, 325, 339, 351] [128, 129, 158, 326, 340, 352] [129, 130, 159, 327, 341, 353] [130, 131, 160, 328, 342, 354] [131, 132, 161, 329, 343, 355] [132, 133, 162, 330, 344, 356] [133, 134, 163, 331, 345, 357] [134, 135, 164, 332, 346, 358] [135, 136, 165, 333, 347, 359] [136, 137, 166, 334, 348, 360] [137, 138, 167, 335, 349, 361] [138, 139, 362] [139, 363] [168, 336, 350] [140, 169, 337, 351] [140, 141, 170, 338, 352, 364] [141, 142, 171, 339, 353, 365] [142, 143, 172, 340, 354, 366] [143, 144, 173, 341, 355, 367] [144, 145, 174, 342, 356, 368] [145, 146, 175, 343, 357, 369] [146, 147, 176, 344, 358, 370] [147, 148, 177, 345, 359, 371] [148, 149, 178, 346, 360, 372] [149, 150, 179, 347, 361, 373] [150, 151, 180, 348, 362, 374] [151, 152, 181, 349, 363, 375] [152, 153, 376] [153, 377] [182, 350, 364] [154, 183, 351, 365] [154, 155, 184, 352, 366, 378] [155, 156, 185, 353, 367, 379] [156, 157, 186, 354, 368, 380] [157, 158, 187, 355, 369, 381] [158, 159, 188, 356, 370, 382] [159, 160, 189, 357, 371, 383] [160, 161, 190, 358, 372, 384] [161, 162, 191, 359, 373, 385] [162, 163, 192, 360, 374, 386] [163, 164, 193, 361, 375, 387] [164, 165, 194, 362, 376, 388] [165, 166, 195, 363, 377, 389] [166, 167, 390] [167, 391]
raw submission JSON