← back to the board
[[390,82,32]] d ≤
n
390
k
82
d
32
kd²/n
215.303
w
16

Share this result

Distance

d_X 32 · witness weight 32 (claimed upper_bound)
witness operator (support, 32 qubits)
[9, 12, 25, 32, 58, 61, 79, 91, 93, 96, 100, 101, 103, 111, 117, 122, 128, 142, 163, 177, 181, 206, 234, 254, 262, 293, 298, 303, 314, 343, 357, 382]
d_Z 32 · witness weight 32 (claimed upper_bound)
witness operator (support, 32 qubits)
[8, 33, 47, 76, 87, 92, 97, 128, 136, 156, 184, 209, 213, 227, 248, 262, 268, 273, 279, 287, 289, 290, 294, 297, 299, 311, 329, 332, 358, 365, 378, 381]
certificate none yet · distance stands as a self-certified upper bound (d ≤)

Construction & provenance

authors @seunomonije
provenance submitted through the challenge
novelty novelty not audited
construction Generalized bicycle code on Z_195 (Panteleev-Kalachev): H_X=[A|B], H_Z=[B^T|A^T] with A, B circulants of a(x) = sum x^i, i in {0,20,51,87,93,103,137,143}; b(x) = sum x^i, i in {0,26,76,88,102,111,123,127}. Both are weight-8 codewords of the classical cyclic code <g> for g = gcd(a, b, x195-1) of degree 41 (the same divisor underlying the [[390,82,30]] board entry), giving k = 2*deg g = 82 by construction. The pool of weight-<=8 codewords of <g> saturates at 12 cyclic-shift classes (60k+ RIS trials, 3 seeds); this pair is one of the 51 previously-unexplored class pairs from the exhaustive 66-pair enumeration of that pool. Distance evidence: staged randomized-information-set ladder 2M/8M/24M trials (fresh seed per rung, pair_depth 8) read 36/36/32; refutation barrage 3x8M trials (seeds 777/999/424242) plus pair_depth-16 and pair_depth-24 passes at 3M trials, and a 48M-trial witness pass: lightest logical ever witnessed has weight 32 (found independently at 24M/seeded ladder and 8M/seed 777). Claimed d <= 32 = the lightest witnessed logical.
model Claude Claude Fable 5 (claimed, not verified)
builds on arXiv:1904.02703
date 2026-07-18
notes Model: Claude Fable 5. Distance is an upper bound from ~124M randomized-information-set trials across 8 independent seeded passes and three pair depths; no logical below weight 32 was ever witnessed.
family generalized bicycle (a tag, not a ranking)
locality unrestricted (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 195 · Z-checks 195
H_X (195 checks, sparse supports)
[0, 20, 51, 87, 93, 103, 137, 143, 195, 221, 271, 283, 297, 306, 318, 322] [1, 21, 52, 88, 94, 104, 138, 144, 196, 222, 272, 284, 298, 307, 319, 323] [2, 22, 53, 89, 95, 105, 139, 145, 197, 223, 273, 285, 299, 308, 320, 324] [3, 23, 54, 90, 96, 106, 140, 146, 198, 224, 274, 286, 300, 309, 321, 325] [4, 24, 55, 91, 97, 107, 141, 147, 199, 225, 275, 287, 301, 310, 322, 326] [5, 25, 56, 92, 98, 108, 142, 148, 200, 226, 276, 288, 302, 311, 323, 327] [6, 26, 57, 93, 99, 109, 143, 149, 201, 227, 277, 289, 303, 312, 324, 328] [7, 27, 58, 94, 100, 110, 144, 150, 202, 228, 278, 290, 304, 313, 325, 329] [8, 28, 59, 95, 101, 111, 145, 151, 203, 229, 279, 291, 305, 314, 326, 330] [9, 29, 60, 96, 102, 112, 146, 152, 204, 230, 280, 292, 306, 315, 327, 331] [10, 30, 61, 97, 103, 113, 147, 153, 205, 231, 281, 293, 307, 316, 328, 332] [11, 31, 62, 98, 104, 114, 148, 154, 206, 232, 282, 294, 308, 317, 329, 333] [12, 32, 63, 99, 105, 115, 149, 155, 207, 233, 283, 295, 309, 318, 330, 334] [13, 33, 64, 100, 106, 116, 150, 156, 208, 234, 284, 296, 310, 319, 331, 335] [14, 34, 65, 101, 107, 117, 151, 157, 209, 235, 285, 297, 311, 320, 332, 336] [15, 35, 66, 102, 108, 118, 152, 158, 210, 236, 286, 298, 312, 321, 333, 337] [16, 36, 67, 103, 109, 119, 153, 159, 211, 237, 287, 299, 313, 322, 334, 338] [17, 37, 68, 104, 110, 120, 154, 160, 212, 238, 288, 300, 314, 323, 335, 339] [18, 38, 69, 105, 111, 121, 155, 161, 213, 239, 289, 301, 315, 324, 336, 340] [19, 39, 70, 106, 112, 122, 156, 162, 214, 240, 290, 302, 316, 325, 337, 341] [20, 40, 71, 107, 113, 123, 157, 163, 215, 241, 291, 303, 317, 326, 338, 342] [21, 41, 72, 108, 114, 124, 158, 164, 216, 242, 292, 304, 318, 327, 339, 343] [22, 42, 73, 109, 115, 125, 159, 165, 217, 243, 293, 305, 319, 328, 340, 344] [23, 43, 74, 110, 116, 126, 160, 166, 218, 244, 294, 306, 320, 329, 341, 345] [24, 44, 75, 111, 117, 127, 161, 167, 219, 245, 295, 307, 321, 330, 342, 346] [25, 45, 76, 112, 118, 128, 162, 168, 220, 246, 296, 308, 322, 331, 343, 347] [26, 46, 77, 113, 119, 129, 163, 169, 221, 247, 297, 309, 323, 332, 344, 348] [27, 47, 78, 114, 120, 130, 164, 170, 222, 248, 298, 310, 324, 333, 345, 349] [28, 48, 79, 115, 121, 131, 165, 171, 223, 249, 299, 311, 325, 334, 346, 350] [29, 49, 80, 116, 122, 132, 166, 172, 224, 250, 300, 312, 326, 335, 347, 351] [30, 50, 81, 117, 123, 133, 167, 173, 225, 251, 301, 313, 327, 336, 348, 352] [31, 51, 82, 118, 124, 134, 168, 174, 226, 252, 302, 314, 328, 337, 349, 353] [32, 52, 83, 119, 125, 135, 169, 175, 227, 253, 303, 315, 329, 338, 350, 354] [33, 53, 84, 120, 126, 136, 170, 176, 228, 254, 304, 316, 330, 339, 351, 355] [34, 54, 85, 121, 127, 137, 171, 177, 229, 255, 305, 317, 331, 340, 352, 356] [35, 55, 86, 122, 128, 138, 172, 178, 230, 256, 306, 318, 332, 341, 353, 357] [36, 56, 87, 123, 129, 139, 173, 179, 231, 257, 307, 319, 333, 342, 354, 358] [37, 57, 88, 124, 130, 140, 174, 180, 232, 258, 308, 320, 334, 343, 355, 359] [38, 58, 89, 125, 131, 141, 175, 181, 233, 259, 309, 321, 335, 344, 356, 360] [39, 59, 90, 126, 132, 142, 176, 182, 234, 260, 310, 322, 336, 345, 357, 361] [40, 60, 91, 127, 133, 143, 177, 183, 235, 261, 311, 323, 337, 346, 358, 362] [41, 61, 92, 128, 134, 144, 178, 184, 236, 262, 312, 324, 338, 347, 359, 363] [42, 62, 93, 129, 135, 145, 179, 185, 237, 263, 313, 325, 339, 348, 360, 364] [43, 63, 94, 130, 136, 146, 180, 186, 238, 264, 314, 326, 340, 349, 361, 365] [44, 64, 95, 131, 137, 147, 181, 187, 239, 265, 315, 327, 341, 350, 362, 366] [45, 65, 96, 132, 138, 148, 182, 188, 240, 266, 316, 328, 342, 351, 363, 367] [46, 66, 97, 133, 139, 149, 183, 189, 241, 267, 317, 329, 343, 352, 364, 368] [47, 67, 98, 134, 140, 150, 184, 190, 242, 268, 318, 330, 344, 353, 365, 369] [48, 68, 99, 135, 141, 151, 185, 191, 243, 269, 319, 331, 345, 354, 366, 370] [49, 69, 100, 136, 142, 152, 186, 192, 244, 270, 320, 332, 346, 355, 367, 371] [50, 70, 101, 137, 143, 153, 187, 193, 245, 271, 321, 333, 347, 356, 368, 372] [51, 71, 102, 138, 144, 154, 188, 194, 246, 272, 322, 334, 348, 357, 369, 373] [0, 52, 72, 103, 139, 145, 155, 189, 247, 273, 323, 335, 349, 358, 370, 374] [1, 53, 73, 104, 140, 146, 156, 190, 248, 274, 324, 336, 350, 359, 371, 375] [2, 54, 74, 105, 141, 147, 157, 191, 249, 275, 325, 337, 351, 360, 372, 376] [3, 55, 75, 106, 142, 148, 158, 192, 250, 276, 326, 338, 352, 361, 373, 377] [4, 56, 76, 107, 143, 149, 159, 193, 251, 277, 327, 339, 353, 362, 374, 378] [5, 57, 77, 108, 144, 150, 160, 194, 252, 278, 328, 340, 354, 363, 375, 379] [0, 6, 58, 78, 109, 145, 151, 161, 253, 279, 329, 341, 355, 364, 376, 380] [1, 7, 59, 79, 110, 146, 152, 162, 254, 280, 330, 342, 356, 365, 377, 381] [2, 8, 60, 80, 111, 147, 153, 163, 255, 281, 331, 343, 357, 366, 378, 382] [3, 9, 61, 81, 112, 148, 154, 164, 256, 282, 332, 344, 358, 367, 379, 383] [4, 10, 62, 82, 113, 149, 155, 165, 257, 283, 333, 345, 359, 368, 380, 384] [5, 11, 63, 83, 114, 150, 156, 166, 258, 284, 334, 346, 360, 369, 381, 385] [6, 12, 64, 84, 115, 151, 157, 167, 259, 285, 335, 347, 361, 370, 382, 386] [7, 13, 65, 85, 116, 152, 158, 168, 260, 286, 336, 348, 362, 371, 383, 387] [8, 14, 66, 86, 117, 153, 159, 169, 261, 287, 337, 349, 363, 372, 384, 388] [9, 15, 67, 87, 118, 154, 160, 170, 262, 288, 338, 350, 364, 373, 385, 389] [10, 16, 68, 88, 119, 155, 161, 171, 195, 263, 289, 339, 351, 365, 374, 386] [11, 17, 69, 89, 120, 156, 162, 172, 196, 264, 290, 340, 352, 366, 375, 387] [12, 18, 70, 90, 121, 157, 163, 173, 197, 265, 291, 341, 353, 367, 376, 388] [13, 19, 71, 91, 122, 158, 164, 174, 198, 266, 292, 342, 354, 368, 377, 389] [14, 20, 72, 92, 123, 159, 165, 175, 195, 199, 267, 293, 343, 355, 369, 378] [15, 21, 73, 93, 124, 160, 166, 176, 196, 200, 268, 294, 344, 356, 370, 379] [16, 22, 74, 94, 125, 161, 167, 177, 197, 201, 269, 295, 345, 357, 371, 380] [17, 23, 75, 95, 126, 162, 168, 178, 198, 202, 270, 296, 346, 358, 372, 381] [18, 24, 76, 96, 127, 163, 169, 179, 199, 203, 271, 297, 347, 359, 373, 382] [19, 25, 77, 97, 128, 164, 170, 180, 200, 204, 272, 298, 348, 360, 374, 383] [20, 26, 78, 98, 129, 165, 171, 181, 201, 205, 273, 299, 349, 361, 375, 384] [21, 27, 79, 99, 130, 166, 172, 182, 202, 206, 274, 300, 350, 362, 376, 385] [22, 28, 80, 100, 131, 167, 173, 183, 203, 207, 275, 301, 351, 363, 377, 386] [23, 29, 81, 101, 132, 168, 174, 184, 204, 208, 276, 302, 352, 364, 378, 387] [24, 30, 82, 102, 133, 169, 175, 185, 205, 209, 277, 303, 353, 365, 379, 388] [25, 31, 83, 103, 134, 170, 176, 186, 206, 210, 278, 304, 354, 366, 380, 389] [26, 32, 84, 104, 135, 171, 177, 187, 195, 207, 211, 279, 305, 355, 367, 381] [27, 33, 85, 105, 136, 172, 178, 188, 196, 208, 212, 280, 306, 356, 368, 382] [28, 34, 86, 106, 137, 173, 179, 189, 197, 209, 213, 281, 307, 357, 369, 383] [29, 35, 87, 107, 138, 174, 180, 190, 198, 210, 214, 282, 308, 358, 370, 384] [30, 36, 88, 108, 139, 175, 181, 191, 199, 211, 215, 283, 309, 359, 371, 385] [31, 37, 89, 109, 140, 176, 182, 192, 200, 212, 216, 284, 310, 360, 372, 386] [32, 38, 90, 110, 141, 177, 183, 193, 201, 213, 217, 285, 311, 361, 373, 387] [33, 39, 91, 111, 142, 178, 184, 194, 202, 214, 218, 286, 312, 362, 374, 388] [0, 34, 40, 92, 112, 143, 179, 185, 203, 215, 219, 287, 313, 363, 375, 389] [1, 35, 41, 93, 113, 144, 180, 186, 195, 204, 216, 220, 288, 314, 364, 376] [2, 36, 42, 94, 114, 145, 181, 187, 196, 205, 217, 221, 289, 315, 365, 377] [3, 37, 43, 95, 115, 146, 182, 188, 197, 206, 218, 222, 290, 316, 366, 378] [4, 38, 44, 96, 116, 147, 183, 189, 198, 207, 219, 223, 291, 317, 367, 379] [5, 39, 45, 97, 117, 148, 184, 190, 199, 208, 220, 224, 292, 318, 368, 380] [6, 40, 46, 98, 118, 149, 185, 191, 200, 209, 221, 225, 293, 319, 369, 381] [7, 41, 47, 99, 119, 150, 186, 192, 201, 210, 222, 226, 294, 320, 370, 382] [8, 42, 48, 100, 120, 151, 187, 193, 202, 211, 223, 227, 295, 321, 371, 383] [9, 43, 49, 101, 121, 152, 188, 194, 203, 212, 224, 228, 296, 322, 372, 384] [0, 10, 44, 50, 102, 122, 153, 189, 204, 213, 225, 229, 297, 323, 373, 385] [1, 11, 45, 51, 103, 123, 154, 190, 205, 214, 226, 230, 298, 324, 374, 386] [2, 12, 46, 52, 104, 124, 155, 191, 206, 215, 227, 231, 299, 325, 375, 387] [3, 13, 47, 53, 105, 125, 156, 192, 207, 216, 228, 232, 300, 326, 376, 388] [4, 14, 48, 54, 106, 126, 157, 193, 208, 217, 229, 233, 301, 327, 377, 389] [5, 15, 49, 55, 107, 127, 158, 194, 195, 209, 218, 230, 234, 302, 328, 378] [0, 6, 16, 50, 56, 108, 128, 159, 196, 210, 219, 231, 235, 303, 329, 379] [1, 7, 17, 51, 57, 109, 129, 160, 197, 211, 220, 232, 236, 304, 330, 380] [2, 8, 18, 52, 58, 110, 130, 161, 198, 212, 221, 233, 237, 305, 331, 381] [3, 9, 19, 53, 59, 111, 131, 162, 199, 213, 222, 234, 238, 306, 332, 382] [4, 10, 20, 54, 60, 112, 132, 163, 200, 214, 223, 235, 239, 307, 333, 383] [5, 11, 21, 55, 61, 113, 133, 164, 201, 215, 224, 236, 240, 308, 334, 384] [6, 12, 22, 56, 62, 114, 134, 165, 202, 216, 225, 237, 241, 309, 335, 385] [7, 13, 23, 57, 63, 115, 135, 166, 203, 217, 226, 238, 242, 310, 336, 386] [8, 14, 24, 58, 64, 116, 136, 167, 204, 218, 227, 239, 243, 311, 337, 387] [9, 15, 25, 59, 65, 117, 137, 168, 205, 219, 228, 240, 244, 312, 338, 388] [10, 16, 26, 60, 66, 118, 138, 169, 206, 220, 229, 241, 245, 313, 339, 389] [11, 17, 27, 61, 67, 119, 139, 170, 195, 207, 221, 230, 242, 246, 314, 340] [12, 18, 28, 62, 68, 120, 140, 171, 196, 208, 222, 231, 243, 247, 315, 341] [13, 19, 29, 63, 69, 121, 141, 172, 197, 209, 223, 232, 244, 248, 316, 342] [14, 20, 30, 64, 70, 122, 142, 173, 198, 210, 224, 233, 245, 249, 317, 343] [15, 21, 31, 65, 71, 123, 143, 174, 199, 211, 225, 234, 246, 250, 318, 344] [16, 22, 32, 66, 72, 124, 144, 175, 200, 212, 226, 235, 247, 251, 319, 345] [17, 23, 33, 67, 73, 125, 145, 176, 201, 213, 227, 236, 248, 252, 320, 346] [18, 24, 34, 68, 74, 126, 146, 177, 202, 214, 228, 237, 249, 253, 321, 347] [19, 25, 35, 69, 75, 127, 147, 178, 203, 215, 229, 238, 250, 254, 322, 348] [20, 26, 36, 70, 76, 128, 148, 179, 204, 216, 230, 239, 251, 255, 323, 349] [21, 27, 37, 71, 77, 129, 149, 180, 205, 217, 231, 240, 252, 256, 324, 350] [22, 28, 38, 72, 78, 130, 150, 181, 206, 218, 232, 241, 253, 257, 325, 351] [23, 29, 39, 73, 79, 131, 151, 182, 207, 219, 233, 242, 254, 258, 326, 352] [24, 30, 40, 74, 80, 132, 152, 183, 208, 220, 234, 243, 255, 259, 327, 353] [25, 31, 41, 75, 81, 133, 153, 184, 209, 221, 235, 244, 256, 260, 328, 354] [26, 32, 42, 76, 82, 134, 154, 185, 210, 222, 236, 245, 257, 261, 329, 355] [27, 33, 43, 77, 83, 135, 155, 186, 211, 223, 237, 246, 258, 262, 330, 356] [28, 34, 44, 78, 84, 136, 156, 187, 212, 224, 238, 247, 259, 263, 331, 357] [29, 35, 45, 79, 85, 137, 157, 188, 213, 225, 239, 248, 260, 264, 332, 358] [30, 36, 46, 80, 86, 138, 158, 189, 214, 226, 240, 249, 261, 265, 333, 359] [31, 37, 47, 81, 87, 139, 159, 190, 215, 227, 241, 250, 262, 266, 334, 360] [32, 38, 48, 82, 88, 140, 160, 191, 216, 228, 242, 251, 263, 267, 335, 361] [33, 39, 49, 83, 89, 141, 161, 192, 217, 229, 243, 252, 264, 268, 336, 362] [34, 40, 50, 84, 90, 142, 162, 193, 218, 230, 244, 253, 265, 269, 337, 363] [35, 41, 51, 85, 91, 143, 163, 194, 219, 231, 245, 254, 266, 270, 338, 364] [0, 36, 42, 52, 86, 92, 144, 164, 220, 232, 246, 255, 267, 271, 339, 365] [1, 37, 43, 53, 87, 93, 145, 165, 221, 233, 247, 256, 268, 272, 340, 366] [2, 38, 44, 54, 88, 94, 146, 166, 222, 234, 248, 257, 269, 273, 341, 367] [3, 39, 45, 55, 89, 95, 147, 167, 223, 235, 249, 258, 270, 274, 342, 368] [4, 40, 46, 56, 90, 96, 148, 168, 224, 236, 250, 259, 271, 275, 343, 369] [5, 41, 47, 57, 91, 97, 149, 169, 225, 237, 251, 260, 272, 276, 344, 370] [6, 42, 48, 58, 92, 98, 150, 170, 226, 238, 252, 261, 273, 277, 345, 371] [7, 43, 49, 59, 93, 99, 151, 171, 227, 239, 253, 262, 274, 278, 346, 372] [8, 44, 50, 60, 94, 100, 152, 172, 228, 240, 254, 263, 275, 279, 347, 373] [9, 45, 51, 61, 95, 101, 153, 173, 229, 241, 255, 264, 276, 280, 348, 374] [10, 46, 52, 62, 96, 102, 154, 174, 230, 242, 256, 265, 277, 281, 349, 375] [11, 47, 53, 63, 97, 103, 155, 175, 231, 243, 257, 266, 278, 282, 350, 376] [12, 48, 54, 64, 98, 104, 156, 176, 232, 244, 258, 267, 279, 283, 351, 377] [13, 49, 55, 65, 99, 105, 157, 177, 233, 245, 259, 268, 280, 284, 352, 378] [14, 50, 56, 66, 100, 106, 158, 178, 234, 246, 260, 269, 281, 285, 353, 379] [15, 51, 57, 67, 101, 107, 159, 179, 235, 247, 261, 270, 282, 286, 354, 380] [16, 52, 58, 68, 102, 108, 160, 180, 236, 248, 262, 271, 283, 287, 355, 381] [17, 53, 59, 69, 103, 109, 161, 181, 237, 249, 263, 272, 284, 288, 356, 382] [18, 54, 60, 70, 104, 110, 162, 182, 238, 250, 264, 273, 285, 289, 357, 383] [19, 55, 61, 71, 105, 111, 163, 183, 239, 251, 265, 274, 286, 290, 358, 384] [20, 56, 62, 72, 106, 112, 164, 184, 240, 252, 266, 275, 287, 291, 359, 385] [21, 57, 63, 73, 107, 113, 165, 185, 241, 253, 267, 276, 288, 292, 360, 386] [22, 58, 64, 74, 108, 114, 166, 186, 242, 254, 268, 277, 289, 293, 361, 387] [23, 59, 65, 75, 109, 115, 167, 187, 243, 255, 269, 278, 290, 294, 362, 388] [24, 60, 66, 76, 110, 116, 168, 188, 244, 256, 270, 279, 291, 295, 363, 389] [25, 61, 67, 77, 111, 117, 169, 189, 195, 245, 257, 271, 280, 292, 296, 364] [26, 62, 68, 78, 112, 118, 170, 190, 196, 246, 258, 272, 281, 293, 297, 365] [27, 63, 69, 79, 113, 119, 171, 191, 197, 247, 259, 273, 282, 294, 298, 366] [28, 64, 70, 80, 114, 120, 172, 192, 198, 248, 260, 274, 283, 295, 299, 367] [29, 65, 71, 81, 115, 121, 173, 193, 199, 249, 261, 275, 284, 296, 300, 368] [30, 66, 72, 82, 116, 122, 174, 194, 200, 250, 262, 276, 285, 297, 301, 369] [0, 31, 67, 73, 83, 117, 123, 175, 201, 251, 263, 277, 286, 298, 302, 370] [1, 32, 68, 74, 84, 118, 124, 176, 202, 252, 264, 278, 287, 299, 303, 371] [2, 33, 69, 75, 85, 119, 125, 177, 203, 253, 265, 279, 288, 300, 304, 372] [3, 34, 70, 76, 86, 120, 126, 178, 204, 254, 266, 280, 289, 301, 305, 373] [4, 35, 71, 77, 87, 121, 127, 179, 205, 255, 267, 281, 290, 302, 306, 374] [5, 36, 72, 78, 88, 122, 128, 180, 206, 256, 268, 282, 291, 303, 307, 375] [6, 37, 73, 79, 89, 123, 129, 181, 207, 257, 269, 283, 292, 304, 308, 376] [7, 38, 74, 80, 90, 124, 130, 182, 208, 258, 270, 284, 293, 305, 309, 377] [8, 39, 75, 81, 91, 125, 131, 183, 209, 259, 271, 285, 294, 306, 310, 378] [9, 40, 76, 82, 92, 126, 132, 184, 210, 260, 272, 286, 295, 307, 311, 379] [10, 41, 77, 83, 93, 127, 133, 185, 211, 261, 273, 287, 296, 308, 312, 380] [11, 42, 78, 84, 94, 128, 134, 186, 212, 262, 274, 288, 297, 309, 313, 381] [12, 43, 79, 85, 95, 129, 135, 187, 213, 263, 275, 289, 298, 310, 314, 382] [13, 44, 80, 86, 96, 130, 136, 188, 214, 264, 276, 290, 299, 311, 315, 383] [14, 45, 81, 87, 97, 131, 137, 189, 215, 265, 277, 291, 300, 312, 316, 384] [15, 46, 82, 88, 98, 132, 138, 190, 216, 266, 278, 292, 301, 313, 317, 385] [16, 47, 83, 89, 99, 133, 139, 191, 217, 267, 279, 293, 302, 314, 318, 386] [17, 48, 84, 90, 100, 134, 140, 192, 218, 268, 280, 294, 303, 315, 319, 387] [18, 49, 85, 91, 101, 135, 141, 193, 219, 269, 281, 295, 304, 316, 320, 388] [19, 50, 86, 92, 102, 136, 142, 194, 220, 270, 282, 296, 305, 317, 321, 389]
H_Z (195 checks, sparse supports)
[0, 68, 72, 84, 93, 107, 119, 169, 195, 247, 253, 287, 297, 303, 339, 370] [1, 69, 73, 85, 94, 108, 120, 170, 196, 248, 254, 288, 298, 304, 340, 371] [2, 70, 74, 86, 95, 109, 121, 171, 197, 249, 255, 289, 299, 305, 341, 372] [3, 71, 75, 87, 96, 110, 122, 172, 198, 250, 256, 290, 300, 306, 342, 373] [4, 72, 76, 88, 97, 111, 123, 173, 199, 251, 257, 291, 301, 307, 343, 374] [5, 73, 77, 89, 98, 112, 124, 174, 200, 252, 258, 292, 302, 308, 344, 375] [6, 74, 78, 90, 99, 113, 125, 175, 201, 253, 259, 293, 303, 309, 345, 376] [7, 75, 79, 91, 100, 114, 126, 176, 202, 254, 260, 294, 304, 310, 346, 377] [8, 76, 80, 92, 101, 115, 127, 177, 203, 255, 261, 295, 305, 311, 347, 378] [9, 77, 81, 93, 102, 116, 128, 178, 204, 256, 262, 296, 306, 312, 348, 379] [10, 78, 82, 94, 103, 117, 129, 179, 205, 257, 263, 297, 307, 313, 349, 380] [11, 79, 83, 95, 104, 118, 130, 180, 206, 258, 264, 298, 308, 314, 350, 381] [12, 80, 84, 96, 105, 119, 131, 181, 207, 259, 265, 299, 309, 315, 351, 382] [13, 81, 85, 97, 106, 120, 132, 182, 208, 260, 266, 300, 310, 316, 352, 383] [14, 82, 86, 98, 107, 121, 133, 183, 209, 261, 267, 301, 311, 317, 353, 384] [15, 83, 87, 99, 108, 122, 134, 184, 210, 262, 268, 302, 312, 318, 354, 385] [16, 84, 88, 100, 109, 123, 135, 185, 211, 263, 269, 303, 313, 319, 355, 386] [17, 85, 89, 101, 110, 124, 136, 186, 212, 264, 270, 304, 314, 320, 356, 387] [18, 86, 90, 102, 111, 125, 137, 187, 213, 265, 271, 305, 315, 321, 357, 388] [19, 87, 91, 103, 112, 126, 138, 188, 214, 266, 272, 306, 316, 322, 358, 389] [20, 88, 92, 104, 113, 127, 139, 189, 195, 215, 267, 273, 307, 317, 323, 359] [21, 89, 93, 105, 114, 128, 140, 190, 196, 216, 268, 274, 308, 318, 324, 360] [22, 90, 94, 106, 115, 129, 141, 191, 197, 217, 269, 275, 309, 319, 325, 361] [23, 91, 95, 107, 116, 130, 142, 192, 198, 218, 270, 276, 310, 320, 326, 362] [24, 92, 96, 108, 117, 131, 143, 193, 199, 219, 271, 277, 311, 321, 327, 363] [25, 93, 97, 109, 118, 132, 144, 194, 200, 220, 272, 278, 312, 322, 328, 364] [0, 26, 94, 98, 110, 119, 133, 145, 201, 221, 273, 279, 313, 323, 329, 365] [1, 27, 95, 99, 111, 120, 134, 146, 202, 222, 274, 280, 314, 324, 330, 366] [2, 28, 96, 100, 112, 121, 135, 147, 203, 223, 275, 281, 315, 325, 331, 367] [3, 29, 97, 101, 113, 122, 136, 148, 204, 224, 276, 282, 316, 326, 332, 368] [4, 30, 98, 102, 114, 123, 137, 149, 205, 225, 277, 283, 317, 327, 333, 369] [5, 31, 99, 103, 115, 124, 138, 150, 206, 226, 278, 284, 318, 328, 334, 370] [6, 32, 100, 104, 116, 125, 139, 151, 207, 227, 279, 285, 319, 329, 335, 371] [7, 33, 101, 105, 117, 126, 140, 152, 208, 228, 280, 286, 320, 330, 336, 372] [8, 34, 102, 106, 118, 127, 141, 153, 209, 229, 281, 287, 321, 331, 337, 373] [9, 35, 103, 107, 119, 128, 142, 154, 210, 230, 282, 288, 322, 332, 338, 374] [10, 36, 104, 108, 120, 129, 143, 155, 211, 231, 283, 289, 323, 333, 339, 375] [11, 37, 105, 109, 121, 130, 144, 156, 212, 232, 284, 290, 324, 334, 340, 376] [12, 38, 106, 110, 122, 131, 145, 157, 213, 233, 285, 291, 325, 335, 341, 377] [13, 39, 107, 111, 123, 132, 146, 158, 214, 234, 286, 292, 326, 336, 342, 378] [14, 40, 108, 112, 124, 133, 147, 159, 215, 235, 287, 293, 327, 337, 343, 379] [15, 41, 109, 113, 125, 134, 148, 160, 216, 236, 288, 294, 328, 338, 344, 380] [16, 42, 110, 114, 126, 135, 149, 161, 217, 237, 289, 295, 329, 339, 345, 381] [17, 43, 111, 115, 127, 136, 150, 162, 218, 238, 290, 296, 330, 340, 346, 382] [18, 44, 112, 116, 128, 137, 151, 163, 219, 239, 291, 297, 331, 341, 347, 383] [19, 45, 113, 117, 129, 138, 152, 164, 220, 240, 292, 298, 332, 342, 348, 384] [20, 46, 114, 118, 130, 139, 153, 165, 221, 241, 293, 299, 333, 343, 349, 385] [21, 47, 115, 119, 131, 140, 154, 166, 222, 242, 294, 300, 334, 344, 350, 386] [22, 48, 116, 120, 132, 141, 155, 167, 223, 243, 295, 301, 335, 345, 351, 387] [23, 49, 117, 121, 133, 142, 156, 168, 224, 244, 296, 302, 336, 346, 352, 388] [24, 50, 118, 122, 134, 143, 157, 169, 225, 245, 297, 303, 337, 347, 353, 389] [25, 51, 119, 123, 135, 144, 158, 170, 195, 226, 246, 298, 304, 338, 348, 354] [26, 52, 120, 124, 136, 145, 159, 171, 196, 227, 247, 299, 305, 339, 349, 355] [27, 53, 121, 125, 137, 146, 160, 172, 197, 228, 248, 300, 306, 340, 350, 356] [28, 54, 122, 126, 138, 147, 161, 173, 198, 229, 249, 301, 307, 341, 351, 357] [29, 55, 123, 127, 139, 148, 162, 174, 199, 230, 250, 302, 308, 342, 352, 358] [30, 56, 124, 128, 140, 149, 163, 175, 200, 231, 251, 303, 309, 343, 353, 359] [31, 57, 125, 129, 141, 150, 164, 176, 201, 232, 252, 304, 310, 344, 354, 360] [32, 58, 126, 130, 142, 151, 165, 177, 202, 233, 253, 305, 311, 345, 355, 361] [33, 59, 127, 131, 143, 152, 166, 178, 203, 234, 254, 306, 312, 346, 356, 362] [34, 60, 128, 132, 144, 153, 167, 179, 204, 235, 255, 307, 313, 347, 357, 363] [35, 61, 129, 133, 145, 154, 168, 180, 205, 236, 256, 308, 314, 348, 358, 364] [36, 62, 130, 134, 146, 155, 169, 181, 206, 237, 257, 309, 315, 349, 359, 365] [37, 63, 131, 135, 147, 156, 170, 182, 207, 238, 258, 310, 316, 350, 360, 366] [38, 64, 132, 136, 148, 157, 171, 183, 208, 239, 259, 311, 317, 351, 361, 367] [39, 65, 133, 137, 149, 158, 172, 184, 209, 240, 260, 312, 318, 352, 362, 368] [40, 66, 134, 138, 150, 159, 173, 185, 210, 241, 261, 313, 319, 353, 363, 369] [41, 67, 135, 139, 151, 160, 174, 186, 211, 242, 262, 314, 320, 354, 364, 370] [42, 68, 136, 140, 152, 161, 175, 187, 212, 243, 263, 315, 321, 355, 365, 371] [43, 69, 137, 141, 153, 162, 176, 188, 213, 244, 264, 316, 322, 356, 366, 372] [44, 70, 138, 142, 154, 163, 177, 189, 214, 245, 265, 317, 323, 357, 367, 373] [45, 71, 139, 143, 155, 164, 178, 190, 215, 246, 266, 318, 324, 358, 368, 374] [46, 72, 140, 144, 156, 165, 179, 191, 216, 247, 267, 319, 325, 359, 369, 375] [47, 73, 141, 145, 157, 166, 180, 192, 217, 248, 268, 320, 326, 360, 370, 376] [48, 74, 142, 146, 158, 167, 181, 193, 218, 249, 269, 321, 327, 361, 371, 377] [49, 75, 143, 147, 159, 168, 182, 194, 219, 250, 270, 322, 328, 362, 372, 378] [0, 50, 76, 144, 148, 160, 169, 183, 220, 251, 271, 323, 329, 363, 373, 379] [1, 51, 77, 145, 149, 161, 170, 184, 221, 252, 272, 324, 330, 364, 374, 380] [2, 52, 78, 146, 150, 162, 171, 185, 222, 253, 273, 325, 331, 365, 375, 381] [3, 53, 79, 147, 151, 163, 172, 186, 223, 254, 274, 326, 332, 366, 376, 382] [4, 54, 80, 148, 152, 164, 173, 187, 224, 255, 275, 327, 333, 367, 377, 383] [5, 55, 81, 149, 153, 165, 174, 188, 225, 256, 276, 328, 334, 368, 378, 384] [6, 56, 82, 150, 154, 166, 175, 189, 226, 257, 277, 329, 335, 369, 379, 385] [7, 57, 83, 151, 155, 167, 176, 190, 227, 258, 278, 330, 336, 370, 380, 386] [8, 58, 84, 152, 156, 168, 177, 191, 228, 259, 279, 331, 337, 371, 381, 387] [9, 59, 85, 153, 157, 169, 178, 192, 229, 260, 280, 332, 338, 372, 382, 388] [10, 60, 86, 154, 158, 170, 179, 193, 230, 261, 281, 333, 339, 373, 383, 389] [11, 61, 87, 155, 159, 171, 180, 194, 195, 231, 262, 282, 334, 340, 374, 384] [0, 12, 62, 88, 156, 160, 172, 181, 196, 232, 263, 283, 335, 341, 375, 385] [1, 13, 63, 89, 157, 161, 173, 182, 197, 233, 264, 284, 336, 342, 376, 386] [2, 14, 64, 90, 158, 162, 174, 183, 198, 234, 265, 285, 337, 343, 377, 387] [3, 15, 65, 91, 159, 163, 175, 184, 199, 235, 266, 286, 338, 344, 378, 388] [4, 16, 66, 92, 160, 164, 176, 185, 200, 236, 267, 287, 339, 345, 379, 389] [5, 17, 67, 93, 161, 165, 177, 186, 195, 201, 237, 268, 288, 340, 346, 380] [6, 18, 68, 94, 162, 166, 178, 187, 196, 202, 238, 269, 289, 341, 347, 381] [7, 19, 69, 95, 163, 167, 179, 188, 197, 203, 239, 270, 290, 342, 348, 382] [8, 20, 70, 96, 164, 168, 180, 189, 198, 204, 240, 271, 291, 343, 349, 383] [9, 21, 71, 97, 165, 169, 181, 190, 199, 205, 241, 272, 292, 344, 350, 384] [10, 22, 72, 98, 166, 170, 182, 191, 200, 206, 242, 273, 293, 345, 351, 385] [11, 23, 73, 99, 167, 171, 183, 192, 201, 207, 243, 274, 294, 346, 352, 386] [12, 24, 74, 100, 168, 172, 184, 193, 202, 208, 244, 275, 295, 347, 353, 387] [13, 25, 75, 101, 169, 173, 185, 194, 203, 209, 245, 276, 296, 348, 354, 388] [0, 14, 26, 76, 102, 170, 174, 186, 204, 210, 246, 277, 297, 349, 355, 389] [1, 15, 27, 77, 103, 171, 175, 187, 195, 205, 211, 247, 278, 298, 350, 356] [2, 16, 28, 78, 104, 172, 176, 188, 196, 206, 212, 248, 279, 299, 351, 357] [3, 17, 29, 79, 105, 173, 177, 189, 197, 207, 213, 249, 280, 300, 352, 358] [4, 18, 30, 80, 106, 174, 178, 190, 198, 208, 214, 250, 281, 301, 353, 359] [5, 19, 31, 81, 107, 175, 179, 191, 199, 209, 215, 251, 282, 302, 354, 360] [6, 20, 32, 82, 108, 176, 180, 192, 200, 210, 216, 252, 283, 303, 355, 361] [7, 21, 33, 83, 109, 177, 181, 193, 201, 211, 217, 253, 284, 304, 356, 362] [8, 22, 34, 84, 110, 178, 182, 194, 202, 212, 218, 254, 285, 305, 357, 363] [0, 9, 23, 35, 85, 111, 179, 183, 203, 213, 219, 255, 286, 306, 358, 364] [1, 10, 24, 36, 86, 112, 180, 184, 204, 214, 220, 256, 287, 307, 359, 365] [2, 11, 25, 37, 87, 113, 181, 185, 205, 215, 221, 257, 288, 308, 360, 366] [3, 12, 26, 38, 88, 114, 182, 186, 206, 216, 222, 258, 289, 309, 361, 367] [4, 13, 27, 39, 89, 115, 183, 187, 207, 217, 223, 259, 290, 310, 362, 368] [5, 14, 28, 40, 90, 116, 184, 188, 208, 218, 224, 260, 291, 311, 363, 369] [6, 15, 29, 41, 91, 117, 185, 189, 209, 219, 225, 261, 292, 312, 364, 370] [7, 16, 30, 42, 92, 118, 186, 190, 210, 220, 226, 262, 293, 313, 365, 371] [8, 17, 31, 43, 93, 119, 187, 191, 211, 221, 227, 263, 294, 314, 366, 372] [9, 18, 32, 44, 94, 120, 188, 192, 212, 222, 228, 264, 295, 315, 367, 373] [10, 19, 33, 45, 95, 121, 189, 193, 213, 223, 229, 265, 296, 316, 368, 374] [11, 20, 34, 46, 96, 122, 190, 194, 214, 224, 230, 266, 297, 317, 369, 375] [0, 12, 21, 35, 47, 97, 123, 191, 215, 225, 231, 267, 298, 318, 370, 376] [1, 13, 22, 36, 48, 98, 124, 192, 216, 226, 232, 268, 299, 319, 371, 377] [2, 14, 23, 37, 49, 99, 125, 193, 217, 227, 233, 269, 300, 320, 372, 378] [3, 15, 24, 38, 50, 100, 126, 194, 218, 228, 234, 270, 301, 321, 373, 379] [0, 4, 16, 25, 39, 51, 101, 127, 219, 229, 235, 271, 302, 322, 374, 380] [1, 5, 17, 26, 40, 52, 102, 128, 220, 230, 236, 272, 303, 323, 375, 381] [2, 6, 18, 27, 41, 53, 103, 129, 221, 231, 237, 273, 304, 324, 376, 382] [3, 7, 19, 28, 42, 54, 104, 130, 222, 232, 238, 274, 305, 325, 377, 383] [4, 8, 20, 29, 43, 55, 105, 131, 223, 233, 239, 275, 306, 326, 378, 384] [5, 9, 21, 30, 44, 56, 106, 132, 224, 234, 240, 276, 307, 327, 379, 385] [6, 10, 22, 31, 45, 57, 107, 133, 225, 235, 241, 277, 308, 328, 380, 386] [7, 11, 23, 32, 46, 58, 108, 134, 226, 236, 242, 278, 309, 329, 381, 387] [8, 12, 24, 33, 47, 59, 109, 135, 227, 237, 243, 279, 310, 330, 382, 388] [9, 13, 25, 34, 48, 60, 110, 136, 228, 238, 244, 280, 311, 331, 383, 389] [10, 14, 26, 35, 49, 61, 111, 137, 195, 229, 239, 245, 281, 312, 332, 384] [11, 15, 27, 36, 50, 62, 112, 138, 196, 230, 240, 246, 282, 313, 333, 385] [12, 16, 28, 37, 51, 63, 113, 139, 197, 231, 241, 247, 283, 314, 334, 386] [13, 17, 29, 38, 52, 64, 114, 140, 198, 232, 242, 248, 284, 315, 335, 387] [14, 18, 30, 39, 53, 65, 115, 141, 199, 233, 243, 249, 285, 316, 336, 388] [15, 19, 31, 40, 54, 66, 116, 142, 200, 234, 244, 250, 286, 317, 337, 389] [16, 20, 32, 41, 55, 67, 117, 143, 195, 201, 235, 245, 251, 287, 318, 338] [17, 21, 33, 42, 56, 68, 118, 144, 196, 202, 236, 246, 252, 288, 319, 339] [18, 22, 34, 43, 57, 69, 119, 145, 197, 203, 237, 247, 253, 289, 320, 340] [19, 23, 35, 44, 58, 70, 120, 146, 198, 204, 238, 248, 254, 290, 321, 341] [20, 24, 36, 45, 59, 71, 121, 147, 199, 205, 239, 249, 255, 291, 322, 342] [21, 25, 37, 46, 60, 72, 122, 148, 200, 206, 240, 250, 256, 292, 323, 343] [22, 26, 38, 47, 61, 73, 123, 149, 201, 207, 241, 251, 257, 293, 324, 344] [23, 27, 39, 48, 62, 74, 124, 150, 202, 208, 242, 252, 258, 294, 325, 345] [24, 28, 40, 49, 63, 75, 125, 151, 203, 209, 243, 253, 259, 295, 326, 346] [25, 29, 41, 50, 64, 76, 126, 152, 204, 210, 244, 254, 260, 296, 327, 347] [26, 30, 42, 51, 65, 77, 127, 153, 205, 211, 245, 255, 261, 297, 328, 348] [27, 31, 43, 52, 66, 78, 128, 154, 206, 212, 246, 256, 262, 298, 329, 349] [28, 32, 44, 53, 67, 79, 129, 155, 207, 213, 247, 257, 263, 299, 330, 350] [29, 33, 45, 54, 68, 80, 130, 156, 208, 214, 248, 258, 264, 300, 331, 351] [30, 34, 46, 55, 69, 81, 131, 157, 209, 215, 249, 259, 265, 301, 332, 352] [31, 35, 47, 56, 70, 82, 132, 158, 210, 216, 250, 260, 266, 302, 333, 353] [32, 36, 48, 57, 71, 83, 133, 159, 211, 217, 251, 261, 267, 303, 334, 354] [33, 37, 49, 58, 72, 84, 134, 160, 212, 218, 252, 262, 268, 304, 335, 355] [34, 38, 50, 59, 73, 85, 135, 161, 213, 219, 253, 263, 269, 305, 336, 356] [35, 39, 51, 60, 74, 86, 136, 162, 214, 220, 254, 264, 270, 306, 337, 357] [36, 40, 52, 61, 75, 87, 137, 163, 215, 221, 255, 265, 271, 307, 338, 358] [37, 41, 53, 62, 76, 88, 138, 164, 216, 222, 256, 266, 272, 308, 339, 359] [38, 42, 54, 63, 77, 89, 139, 165, 217, 223, 257, 267, 273, 309, 340, 360] [39, 43, 55, 64, 78, 90, 140, 166, 218, 224, 258, 268, 274, 310, 341, 361] [40, 44, 56, 65, 79, 91, 141, 167, 219, 225, 259, 269, 275, 311, 342, 362] [41, 45, 57, 66, 80, 92, 142, 168, 220, 226, 260, 270, 276, 312, 343, 363] [42, 46, 58, 67, 81, 93, 143, 169, 221, 227, 261, 271, 277, 313, 344, 364] [43, 47, 59, 68, 82, 94, 144, 170, 222, 228, 262, 272, 278, 314, 345, 365] [44, 48, 60, 69, 83, 95, 145, 171, 223, 229, 263, 273, 279, 315, 346, 366] [45, 49, 61, 70, 84, 96, 146, 172, 224, 230, 264, 274, 280, 316, 347, 367] [46, 50, 62, 71, 85, 97, 147, 173, 225, 231, 265, 275, 281, 317, 348, 368] [47, 51, 63, 72, 86, 98, 148, 174, 226, 232, 266, 276, 282, 318, 349, 369] [48, 52, 64, 73, 87, 99, 149, 175, 227, 233, 267, 277, 283, 319, 350, 370] [49, 53, 65, 74, 88, 100, 150, 176, 228, 234, 268, 278, 284, 320, 351, 371] [50, 54, 66, 75, 89, 101, 151, 177, 229, 235, 269, 279, 285, 321, 352, 372] [51, 55, 67, 76, 90, 102, 152, 178, 230, 236, 270, 280, 286, 322, 353, 373] [52, 56, 68, 77, 91, 103, 153, 179, 231, 237, 271, 281, 287, 323, 354, 374] [53, 57, 69, 78, 92, 104, 154, 180, 232, 238, 272, 282, 288, 324, 355, 375] [54, 58, 70, 79, 93, 105, 155, 181, 233, 239, 273, 283, 289, 325, 356, 376] [55, 59, 71, 80, 94, 106, 156, 182, 234, 240, 274, 284, 290, 326, 357, 377] [56, 60, 72, 81, 95, 107, 157, 183, 235, 241, 275, 285, 291, 327, 358, 378] [57, 61, 73, 82, 96, 108, 158, 184, 236, 242, 276, 286, 292, 328, 359, 379] [58, 62, 74, 83, 97, 109, 159, 185, 237, 243, 277, 287, 293, 329, 360, 380] [59, 63, 75, 84, 98, 110, 160, 186, 238, 244, 278, 288, 294, 330, 361, 381] [60, 64, 76, 85, 99, 111, 161, 187, 239, 245, 279, 289, 295, 331, 362, 382] [61, 65, 77, 86, 100, 112, 162, 188, 240, 246, 280, 290, 296, 332, 363, 383] [62, 66, 78, 87, 101, 113, 163, 189, 241, 247, 281, 291, 297, 333, 364, 384] [63, 67, 79, 88, 102, 114, 164, 190, 242, 248, 282, 292, 298, 334, 365, 385] [64, 68, 80, 89, 103, 115, 165, 191, 243, 249, 283, 293, 299, 335, 366, 386] [65, 69, 81, 90, 104, 116, 166, 192, 244, 250, 284, 294, 300, 336, 367, 387] [66, 70, 82, 91, 105, 117, 167, 193, 245, 251, 285, 295, 301, 337, 368, 388] [67, 71, 83, 92, 106, 118, 168, 194, 246, 252, 286, 296, 302, 338, 369, 389]
raw submission JSON