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[[663,351,10]] d ≤
n
663
k
351
d
10
kd²/n
52.941
w
25
X/Z
1

Share this result

Distance

X/Z asymmetry 1 · d_X ≤ 10, d_Z ≤ 10 · w_X = 25, w_Z = 25 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)
d_X 10 · witness weight 10 (claimed upper_bound)
witness operator (support, 10 qubits)
[0, 1, 6, 13, 23, 39, 41, 45, 50, 56]
d_Z 10 · witness weight 10 (claimed upper_bound)
witness operator (support, 10 qubits)
[0, 17, 23, 24, 32, 156, 178, 180, 181, 192]
certificate none yet · distance stands as a self-certified upper bound (d ≤)

Diagnostics

computed by the verifier from the parity checks, the layout, and the stored witnesses; shown as evidence, not used for ranking
girth H_X 4 · H_Z 4 (shortest cycle of each side’s Tanner graph; longer is friendlier to belief propagation)
check weights H_X 25 · H_Z 25
qubit degrees H_X 5–20 (mean 5.882) · H_Z 5–20 (mean 5.882)
trapping sets H_X (1,5)×624 (2,4)×312 (smallest syndrome weight at each size, connected sets of up to 3 qubits; sizes above 2 skipped under the cost cap)
full (size, syndrome weight): count census for H_X
(1,5): 624 (1,20): 39 (2,4): 312 (2,6): 4212 (2,8): 20280 (2,19): 312 (2,21): 2496 (2,23): 9672 (2,32): 39 (2,34): 273 (2,36): 234 (2,38): 117
trapping sets H_Z (1,5)×624 (2,4)×312 (smallest syndrome weight at each size, connected sets of up to 3 qubits; sizes above 2 skipped under the cost cap)
full (size, syndrome weight): count census for H_Z
(1,5): 624 (1,20): 39 (2,4): 312 (2,6): 4212 (2,8): 20280 (2,19): 312 (2,21): 2496 (2,23): 9672 (2,32): 39 (2,34): 273 (2,36): 234 (2,38): 117

Construction & provenance

authors @hirobumii
provenance submitted through the challenge
novelty novelty not audited
construction C39 scalar1x4 cross product. X[j,r]: VV(k,j,r+g),g in A_k; CC(r+g),g in B_j. Z[k,r]: VV(k,j,r-g),g in B_j; CC(r-g),g in A_k. A supports=[[0, 3, 14, 15, 17], [0, 7, 15, 16, 22], [0, 6, 11, 19, 22], [0, 7, 9, 15, 27]]; B supports=[[0, 2, 6, 11, 17], [0, 1, 6, 13, 23], [0, 2, 9, 14, 23], [0, 1, 4, 16, 25]]. Every individual entry is invertible.
model GPT-6 Astra + GPT-6.1 Sol (recorded multi-agent configuration) (claimed, not verified)
builds on https://arxiv.org/abs/2111.03654
date 2026-10-18
notes Displayed presentation: maximum check weight 25, maximum qubit degree 40, 312 checks and total incidence 7800.
family lifted product (a tag, not a ranking)
locality unrestricted (computed from the layout)
weight class weight > 8 (computed)

How this code was found

the research note submitted with this code · raw markdown · all notes

[[663,351,10]] - CSS sparse stabilizer code

Direction & hypothesis

Study sparse finite instances of the construction below and their dimension–distance tradeoff.

What was searched

C39 scalar1x4 cross product. X[j,r]: VV(k,j,r+g),g in A_k; CC(r+g),g in B_j. Z[k,r]: VV(k,j,r-g),g in B_j; CC(r-g),g in A_k. A supports=[[0, 3, 14, 15, 17], [0, 7, 15, 16, 22], [0, 6, 11, 19, 22], [0, 7, 9, 15, 27]]; B supports=[[0, 2, 6, 11, 17], [0, 1, 6, 13, 23], [0, 2, 9, 14, 23], [0, 1, 4, 16, 25]]. Every individual entry is invertible.

The displayed presentation has maximum check weight 25, maximum qubit degree 40, 312 checks and total incidence 7800.

Evidence trail

The JSON contains weight-10 logical witnesses. Distance confidence: X: upper_bound, Z: upper_bound.

Tools

Recorded workflow configuration: GPT-6 Astra + GPT-6.1 Sol. Official tooling: verify/qldpc_verify.py.

Reproduction

Read codes/663-351-10.json. Allocate zero binary matrices H_X and H_Z with 663 columns. For each row list in checks.X or checks.Z, set the listed zero-based columns to 1, preserving row order. This reconstructs the displayed presentation exactly.

Construction references:

  • https://arxiv.org/abs/2111.03654

Local validation: the official verify/validate_candidate.py passed, including independent-seed distance refutation.

Parity checks

X-checks 156 (max weight 25) · Z-checks 156 (max weight 25)
H_X (156 checks, sparse supports)
[0, 3, 14, 15, 17, 156, 163, 171, 172, 178, 312, 318, 323, 331, 334, 468, 475, 477, 483, 495, 624, 626, 630, 635, 641] [1, 4, 15, 16, 18, 157, 164, 172, 173, 179, 313, 319, 324, 332, 335, 469, 476, 478, 484, 496, 625, 627, 631, 636, 642] [2, 5, 16, 17, 19, 158, 165, 173, 174, 180, 314, 320, 325, 333, 336, 470, 477, 479, 485, 497, 626, 628, 632, 637, 643] [3, 6, 17, 18, 20, 159, 166, 174, 175, 181, 315, 321, 326, 334, 337, 471, 478, 480, 486, 498, 627, 629, 633, 638, 644] [4, 7, 18, 19, 21, 160, 167, 175, 176, 182, 316, 322, 327, 335, 338, 472, 479, 481, 487, 499, 628, 630, 634, 639, 645] [5, 8, 19, 20, 22, 161, 168, 176, 177, 183, 317, 323, 328, 336, 339, 473, 480, 482, 488, 500, 629, 631, 635, 640, 646] [6, 9, 20, 21, 23, 162, 169, 177, 178, 184, 318, 324, 329, 337, 340, 474, 481, 483, 489, 501, 630, 632, 636, 641, 647] [7, 10, 21, 22, 24, 163, 170, 178, 179, 185, 319, 325, 330, 338, 341, 475, 482, 484, 490, 502, 631, 633, 637, 642, 648] [8, 11, 22, 23, 25, 164, 171, 179, 180, 186, 320, 326, 331, 339, 342, 476, 483, 485, 491, 503, 632, 634, 638, 643, 649] [9, 12, 23, 24, 26, 165, 172, 180, 181, 187, 321, 327, 332, 340, 343, 477, 484, 486, 492, 504, 633, 635, 639, 644, 650] [10, 13, 24, 25, 27, 166, 173, 181, 182, 188, 322, 328, 333, 341, 344, 478, 485, 487, 493, 505, 634, 636, 640, 645, 651] [11, 14, 25, 26, 28, 167, 174, 182, 183, 189, 323, 329, 334, 342, 345, 479, 486, 488, 494, 506, 635, 637, 641, 646, 652] [12, 15, 26, 27, 29, 168, 175, 183, 184, 190, 324, 330, 335, 343, 346, 468, 480, 487, 489, 495, 636, 638, 642, 647, 653] [13, 16, 27, 28, 30, 169, 176, 184, 185, 191, 325, 331, 336, 344, 347, 469, 481, 488, 490, 496, 637, 639, 643, 648, 654] [14, 17, 28, 29, 31, 170, 177, 185, 186, 192, 326, 332, 337, 345, 348, 470, 482, 489, 491, 497, 638, 640, 644, 649, 655] [15, 18, 29, 30, 32, 171, 178, 186, 187, 193, 327, 333, 338, 346, 349, 471, 483, 490, 492, 498, 639, 641, 645, 650, 656] [16, 19, 30, 31, 33, 172, 179, 187, 188, 194, 328, 334, 339, 347, 350, 472, 484, 491, 493, 499, 640, 642, 646, 651, 657] [17, 20, 31, 32, 34, 156, 173, 180, 188, 189, 312, 329, 335, 340, 348, 473, 485, 492, 494, 500, 641, 643, 647, 652, 658] [18, 21, 32, 33, 35, 157, 174, 181, 189, 190, 313, 330, 336, 341, 349, 474, 486, 493, 495, 501, 642, 644, 648, 653, 659] [19, 22, 33, 34, 36, 158, 175, 182, 190, 191, 314, 331, 337, 342, 350, 475, 487, 494, 496, 502, 643, 645, 649, 654, 660] [20, 23, 34, 35, 37, 159, 176, 183, 191, 192, 312, 315, 332, 338, 343, 476, 488, 495, 497, 503, 644, 646, 650, 655, 661] [21, 24, 35, 36, 38, 160, 177, 184, 192, 193, 313, 316, 333, 339, 344, 477, 489, 496, 498, 504, 645, 647, 651, 656, 662] [0, 22, 25, 36, 37, 161, 178, 185, 193, 194, 314, 317, 334, 340, 345, 478, 490, 497, 499, 505, 624, 646, 648, 652, 657] [1, 23, 26, 37, 38, 156, 162, 179, 186, 194, 315, 318, 335, 341, 346, 479, 491, 498, 500, 506, 625, 647, 649, 653, 658] [0, 2, 24, 27, 38, 156, 157, 163, 180, 187, 316, 319, 336, 342, 347, 468, 480, 492, 499, 501, 626, 648, 650, 654, 659] [0, 1, 3, 25, 28, 157, 158, 164, 181, 188, 317, 320, 337, 343, 348, 469, 481, 493, 500, 502, 627, 649, 651, 655, 660] [1, 2, 4, 26, 29, 158, 159, 165, 182, 189, 318, 321, 338, 344, 349, 470, 482, 494, 501, 503, 628, 650, 652, 656, 661] [2, 3, 5, 27, 30, 159, 160, 166, 183, 190, 319, 322, 339, 345, 350, 471, 483, 495, 502, 504, 629, 651, 653, 657, 662] [3, 4, 6, 28, 31, 160, 161, 167, 184, 191, 312, 320, 323, 340, 346, 472, 484, 496, 503, 505, 624, 630, 652, 654, 658] [4, 5, 7, 29, 32, 161, 162, 168, 185, 192, 313, 321, 324, 341, 347, 473, 485, 497, 504, 506, 625, 631, 653, 655, 659] [5, 6, 8, 30, 33, 162, 163, 169, 186, 193, 314, 322, 325, 342, 348, 468, 474, 486, 498, 505, 626, 632, 654, 656, 660] [6, 7, 9, 31, 34, 163, 164, 170, 187, 194, 315, 323, 326, 343, 349, 469, 475, 487, 499, 506, 627, 633, 655, 657, 661] [7, 8, 10, 32, 35, 156, 164, 165, 171, 188, 316, 324, 327, 344, 350, 468, 470, 476, 488, 500, 628, 634, 656, 658, 662] [8, 9, 11, 33, 36, 157, 165, 166, 172, 189, 312, 317, 325, 328, 345, 469, 471, 477, 489, 501, 624, 629, 635, 657, 659] [9, 10, 12, 34, 37, 158, 166, 167, 173, 190, 313, 318, 326, 329, 346, 470, 472, 478, 490, 502, 625, 630, 636, 658, 660] [10, 11, 13, 35, 38, 159, 167, 168, 174, 191, 314, 319, 327, 330, 347, 471, 473, 479, 491, 503, 626, 631, 637, 659, 661] [0, 11, 12, 14, 36, 160, 168, 169, 175, 192, 315, 320, 328, 331, 348, 472, 474, 480, 492, 504, 627, 632, 638, 660, 662] [1, 12, 13, 15, 37, 161, 169, 170, 176, 193, 316, 321, 329, 332, 349, 473, 475, 481, 493, 505, 624, 628, 633, 639, 661] [2, 13, 14, 16, 38, 162, 170, 171, 177, 194, 317, 322, 330, 333, 350, 474, 476, 482, 494, 506, 625, 629, 634, 640, 662] [39, 42, 53, 54, 56, 195, 202, 210, 211, 217, 351, 357, 362, 370, 373, 507, 514, 516, 522, 534, 624, 625, 630, 637, 647] [40, 43, 54, 55, 57, 196, 203, 211, 212, 218, 352, 358, 363, 371, 374, 508, 515, 517, 523, 535, 625, 626, 631, 638, 648] [41, 44, 55, 56, 58, 197, 204, 212, 213, 219, 353, 359, 364, 372, 375, 509, 516, 518, 524, 536, 626, 627, 632, 639, 649] [42, 45, 56, 57, 59, 198, 205, 213, 214, 220, 354, 360, 365, 373, 376, 510, 517, 519, 525, 537, 627, 628, 633, 640, 650] [43, 46, 57, 58, 60, 199, 206, 214, 215, 221, 355, 361, 366, 374, 377, 511, 518, 520, 526, 538, 628, 629, 634, 641, 651] [44, 47, 58, 59, 61, 200, 207, 215, 216, 222, 356, 362, 367, 375, 378, 512, 519, 521, 527, 539, 629, 630, 635, 642, 652] [45, 48, 59, 60, 62, 201, 208, 216, 217, 223, 357, 363, 368, 376, 379, 513, 520, 522, 528, 540, 630, 631, 636, 643, 653] [46, 49, 60, 61, 63, 202, 209, 217, 218, 224, 358, 364, 369, 377, 380, 514, 521, 523, 529, 541, 631, 632, 637, 644, 654] [47, 50, 61, 62, 64, 203, 210, 218, 219, 225, 359, 365, 370, 378, 381, 515, 522, 524, 530, 542, 632, 633, 638, 645, 655] [48, 51, 62, 63, 65, 204, 211, 219, 220, 226, 360, 366, 371, 379, 382, 516, 523, 525, 531, 543, 633, 634, 639, 646, 656] [49, 52, 63, 64, 66, 205, 212, 220, 221, 227, 361, 367, 372, 380, 383, 517, 524, 526, 532, 544, 634, 635, 640, 647, 657] [50, 53, 64, 65, 67, 206, 213, 221, 222, 228, 362, 368, 373, 381, 384, 518, 525, 527, 533, 545, 635, 636, 641, 648, 658] [51, 54, 65, 66, 68, 207, 214, 222, 223, 229, 363, 369, 374, 382, 385, 507, 519, 526, 528, 534, 636, 637, 642, 649, 659] [52, 55, 66, 67, 69, 208, 215, 223, 224, 230, 364, 370, 375, 383, 386, 508, 520, 527, 529, 535, 637, 638, 643, 650, 660] [53, 56, 67, 68, 70, 209, 216, 224, 225, 231, 365, 371, 376, 384, 387, 509, 521, 528, 530, 536, 638, 639, 644, 651, 661] [54, 57, 68, 69, 71, 210, 217, 225, 226, 232, 366, 372, 377, 385, 388, 510, 522, 529, 531, 537, 639, 640, 645, 652, 662] [55, 58, 69, 70, 72, 211, 218, 226, 227, 233, 367, 373, 378, 386, 389, 511, 523, 530, 532, 538, 624, 640, 641, 646, 653] [56, 59, 70, 71, 73, 195, 212, 219, 227, 228, 351, 368, 374, 379, 387, 512, 524, 531, 533, 539, 625, 641, 642, 647, 654] [57, 60, 71, 72, 74, 196, 213, 220, 228, 229, 352, 369, 375, 380, 388, 513, 525, 532, 534, 540, 626, 642, 643, 648, 655] [58, 61, 72, 73, 75, 197, 214, 221, 229, 230, 353, 370, 376, 381, 389, 514, 526, 533, 535, 541, 627, 643, 644, 649, 656] [59, 62, 73, 74, 76, 198, 215, 222, 230, 231, 351, 354, 371, 377, 382, 515, 527, 534, 536, 542, 628, 644, 645, 650, 657] [60, 63, 74, 75, 77, 199, 216, 223, 231, 232, 352, 355, 372, 378, 383, 516, 528, 535, 537, 543, 629, 645, 646, 651, 658] [39, 61, 64, 75, 76, 200, 217, 224, 232, 233, 353, 356, 373, 379, 384, 517, 529, 536, 538, 544, 630, 646, 647, 652, 659] [40, 62, 65, 76, 77, 195, 201, 218, 225, 233, 354, 357, 374, 380, 385, 518, 530, 537, 539, 545, 631, 647, 648, 653, 660] [39, 41, 63, 66, 77, 195, 196, 202, 219, 226, 355, 358, 375, 381, 386, 507, 519, 531, 538, 540, 632, 648, 649, 654, 661] [39, 40, 42, 64, 67, 196, 197, 203, 220, 227, 356, 359, 376, 382, 387, 508, 520, 532, 539, 541, 633, 649, 650, 655, 662] [40, 41, 43, 65, 68, 197, 198, 204, 221, 228, 357, 360, 377, 383, 388, 509, 521, 533, 540, 542, 624, 634, 650, 651, 656] [41, 42, 44, 66, 69, 198, 199, 205, 222, 229, 358, 361, 378, 384, 389, 510, 522, 534, 541, 543, 625, 635, 651, 652, 657] [42, 43, 45, 67, 70, 199, 200, 206, 223, 230, 351, 359, 362, 379, 385, 511, 523, 535, 542, 544, 626, 636, 652, 653, 658] [43, 44, 46, 68, 71, 200, 201, 207, 224, 231, 352, 360, 363, 380, 386, 512, 524, 536, 543, 545, 627, 637, 653, 654, 659] [44, 45, 47, 69, 72, 201, 202, 208, 225, 232, 353, 361, 364, 381, 387, 507, 513, 525, 537, 544, 628, 638, 654, 655, 660] [45, 46, 48, 70, 73, 202, 203, 209, 226, 233, 354, 362, 365, 382, 388, 508, 514, 526, 538, 545, 629, 639, 655, 656, 661] [46, 47, 49, 71, 74, 195, 203, 204, 210, 227, 355, 363, 366, 383, 389, 507, 509, 515, 527, 539, 630, 640, 656, 657, 662] [47, 48, 50, 72, 75, 196, 204, 205, 211, 228, 351, 356, 364, 367, 384, 508, 510, 516, 528, 540, 624, 631, 641, 657, 658] [48, 49, 51, 73, 76, 197, 205, 206, 212, 229, 352, 357, 365, 368, 385, 509, 511, 517, 529, 541, 625, 632, 642, 658, 659] [49, 50, 52, 74, 77, 198, 206, 207, 213, 230, 353, 358, 366, 369, 386, 510, 512, 518, 530, 542, 626, 633, 643, 659, 660] [39, 50, 51, 53, 75, 199, 207, 208, 214, 231, 354, 359, 367, 370, 387, 511, 513, 519, 531, 543, 627, 634, 644, 660, 661] [40, 51, 52, 54, 76, 200, 208, 209, 215, 232, 355, 360, 368, 371, 388, 512, 514, 520, 532, 544, 628, 635, 645, 661, 662] [41, 52, 53, 55, 77, 201, 209, 210, 216, 233, 356, 361, 369, 372, 389, 513, 515, 521, 533, 545, 624, 629, 636, 646, 662] [78, 81, 92, 93, 95, 234, 241, 249, 250, 256, 390, 396, 401, 409, 412, 546, 553, 555, 561, 573, 624, 626, 633, 638, 647] [79, 82, 93, 94, 96, 235, 242, 250, 251, 257, 391, 397, 402, 410, 413, 547, 554, 556, 562, 574, 625, 627, 634, 639, 648] [80, 83, 94, 95, 97, 236, 243, 251, 252, 258, 392, 398, 403, 411, 414, 548, 555, 557, 563, 575, 626, 628, 635, 640, 649] [81, 84, 95, 96, 98, 237, 244, 252, 253, 259, 393, 399, 404, 412, 415, 549, 556, 558, 564, 576, 627, 629, 636, 641, 650] [82, 85, 96, 97, 99, 238, 245, 253, 254, 260, 394, 400, 405, 413, 416, 550, 557, 559, 565, 577, 628, 630, 637, 642, 651] [83, 86, 97, 98, 100, 239, 246, 254, 255, 261, 395, 401, 406, 414, 417, 551, 558, 560, 566, 578, 629, 631, 638, 643, 652] [84, 87, 98, 99, 101, 240, 247, 255, 256, 262, 396, 402, 407, 415, 418, 552, 559, 561, 567, 579, 630, 632, 639, 644, 653] [85, 88, 99, 100, 102, 241, 248, 256, 257, 263, 397, 403, 408, 416, 419, 553, 560, 562, 568, 580, 631, 633, 640, 645, 654] [86, 89, 100, 101, 103, 242, 249, 257, 258, 264, 398, 404, 409, 417, 420, 554, 561, 563, 569, 581, 632, 634, 641, 646, 655] [87, 90, 101, 102, 104, 243, 250, 258, 259, 265, 399, 405, 410, 418, 421, 555, 562, 564, 570, 582, 633, 635, 642, 647, 656] [88, 91, 102, 103, 105, 244, 251, 259, 260, 266, 400, 406, 411, 419, 422, 556, 563, 565, 571, 583, 634, 636, 643, 648, 657] [89, 92, 103, 104, 106, 245, 252, 260, 261, 267, 401, 407, 412, 420, 423, 557, 564, 566, 572, 584, 635, 637, 644, 649, 658] [90, 93, 104, 105, 107, 246, 253, 261, 262, 268, 402, 408, 413, 421, 424, 546, 558, 565, 567, 573, 636, 638, 645, 650, 659] [91, 94, 105, 106, 108, 247, 254, 262, 263, 269, 403, 409, 414, 422, 425, 547, 559, 566, 568, 574, 637, 639, 646, 651, 660] [92, 95, 106, 107, 109, 248, 255, 263, 264, 270, 404, 410, 415, 423, 426, 548, 560, 567, 569, 575, 638, 640, 647, 652, 661] [93, 96, 107, 108, 110, 249, 256, 264, 265, 271, 405, 411, 416, 424, 427, 549, 561, 568, 570, 576, 639, 641, 648, 653, 662] [94, 97, 108, 109, 111, 250, 257, 265, 266, 272, 406, 412, 417, 425, 428, 550, 562, 569, 571, 577, 624, 640, 642, 649, 654] [95, 98, 109, 110, 112, 234, 251, 258, 266, 267, 390, 407, 413, 418, 426, 551, 563, 570, 572, 578, 625, 641, 643, 650, 655] [96, 99, 110, 111, 113, 235, 252, 259, 267, 268, 391, 408, 414, 419, 427, 552, 564, 571, 573, 579, 626, 642, 644, 651, 656] [97, 100, 111, 112, 114, 236, 253, 260, 268, 269, 392, 409, 415, 420, 428, 553, 565, 572, 574, 580, 627, 643, 645, 652, 657] [98, 101, 112, 113, 115, 237, 254, 261, 269, 270, 390, 393, 410, 416, 421, 554, 566, 573, 575, 581, 628, 644, 646, 653, 658] [99, 102, 113, 114, 116, 238, 255, 262, 270, 271, 391, 394, 411, 417, 422, 555, 567, 574, 576, 582, 629, 645, 647, 654, 659] [78, 100, 103, 114, 115, 239, 256, 263, 271, 272, 392, 395, 412, 418, 423, 556, 568, 575, 577, 583, 630, 646, 648, 655, 660] [79, 101, 104, 115, 116, 234, 240, 257, 264, 272, 393, 396, 413, 419, 424, 557, 569, 576, 578, 584, 631, 647, 649, 656, 661] [78, 80, 102, 105, 116, 234, 235, 241, 258, 265, 394, 397, 414, 420, 425, 546, 558, 570, 577, 579, 632, 648, 650, 657, 662] [78, 79, 81, 103, 106, 235, 236, 242, 259, 266, 395, 398, 415, 421, 426, 547, 559, 571, 578, 580, 624, 633, 649, 651, 658] [79, 80, 82, 104, 107, 236, 237, 243, 260, 267, 396, 399, 416, 422, 427, 548, 560, 572, 579, 581, 625, 634, 650, 652, 659] [80, 81, 83, 105, 108, 237, 238, 244, 261, 268, 397, 400, 417, 423, 428, 549, 561, 573, 580, 582, 626, 635, 651, 653, 660] [81, 82, 84, 106, 109, 238, 239, 245, 262, 269, 390, 398, 401, 418, 424, 550, 562, 574, 581, 583, 627, 636, 652, 654, 661] [82, 83, 85, 107, 110, 239, 240, 246, 263, 270, 391, 399, 402, 419, 425, 551, 563, 575, 582, 584, 628, 637, 653, 655, 662] [83, 84, 86, 108, 111, 240, 241, 247, 264, 271, 392, 400, 403, 420, 426, 546, 552, 564, 576, 583, 624, 629, 638, 654, 656] [84, 85, 87, 109, 112, 241, 242, 248, 265, 272, 393, 401, 404, 421, 427, 547, 553, 565, 577, 584, 625, 630, 639, 655, 657] [85, 86, 88, 110, 113, 234, 242, 243, 249, 266, 394, 402, 405, 422, 428, 546, 548, 554, 566, 578, 626, 631, 640, 656, 658] [86, 87, 89, 111, 114, 235, 243, 244, 250, 267, 390, 395, 403, 406, 423, 547, 549, 555, 567, 579, 627, 632, 641, 657, 659] [87, 88, 90, 112, 115, 236, 244, 245, 251, 268, 391, 396, 404, 407, 424, 548, 550, 556, 568, 580, 628, 633, 642, 658, 660] [88, 89, 91, 113, 116, 237, 245, 246, 252, 269, 392, 397, 405, 408, 425, 549, 551, 557, 569, 581, 629, 634, 643, 659, 661] [78, 89, 90, 92, 114, 238, 246, 247, 253, 270, 393, 398, 406, 409, 426, 550, 552, 558, 570, 582, 630, 635, 644, 660, 662] [79, 90, 91, 93, 115, 239, 247, 248, 254, 271, 394, 399, 407, 410, 427, 551, 553, 559, 571, 583, 624, 631, 636, 645, 661] [80, 91, 92, 94, 116, 240, 248, 249, 255, 272, 395, 400, 408, 411, 428, 552, 554, 560, 572, 584, 625, 632, 637, 646, 662] [117, 120, 131, 132, 134, 273, 280, 288, 289, 295, 429, 435, 440, 448, 451, 585, 592, 594, 600, 612, 624, 625, 628, 640, 649] [118, 121, 132, 133, 135, 274, 281, 289, 290, 296, 430, 436, 441, 449, 452, 586, 593, 595, 601, 613, 625, 626, 629, 641, 650] [119, 122, 133, 134, 136, 275, 282, 290, 291, 297, 431, 437, 442, 450, 453, 587, 594, 596, 602, 614, 626, 627, 630, 642, 651] [120, 123, 134, 135, 137, 276, 283, 291, 292, 298, 432, 438, 443, 451, 454, 588, 595, 597, 603, 615, 627, 628, 631, 643, 652] [121, 124, 135, 136, 138, 277, 284, 292, 293, 299, 433, 439, 444, 452, 455, 589, 596, 598, 604, 616, 628, 629, 632, 644, 653] [122, 125, 136, 137, 139, 278, 285, 293, 294, 300, 434, 440, 445, 453, 456, 590, 597, 599, 605, 617, 629, 630, 633, 645, 654] [123, 126, 137, 138, 140, 279, 286, 294, 295, 301, 435, 441, 446, 454, 457, 591, 598, 600, 606, 618, 630, 631, 634, 646, 655] [124, 127, 138, 139, 141, 280, 287, 295, 296, 302, 436, 442, 447, 455, 458, 592, 599, 601, 607, 619, 631, 632, 635, 647, 656] [125, 128, 139, 140, 142, 281, 288, 296, 297, 303, 437, 443, 448, 456, 459, 593, 600, 602, 608, 620, 632, 633, 636, 648, 657] [126, 129, 140, 141, 143, 282, 289, 297, 298, 304, 438, 444, 449, 457, 460, 594, 601, 603, 609, 621, 633, 634, 637, 649, 658] [127, 130, 141, 142, 144, 283, 290, 298, 299, 305, 439, 445, 450, 458, 461, 595, 602, 604, 610, 622, 634, 635, 638, 650, 659] [128, 131, 142, 143, 145, 284, 291, 299, 300, 306, 440, 446, 451, 459, 462, 596, 603, 605, 611, 623, 635, 636, 639, 651, 660] [129, 132, 143, 144, 146, 285, 292, 300, 301, 307, 441, 447, 452, 460, 463, 585, 597, 604, 606, 612, 636, 637, 640, 652, 661] [130, 133, 144, 145, 147, 286, 293, 301, 302, 308, 442, 448, 453, 461, 464, 586, 598, 605, 607, 613, 637, 638, 641, 653, 662] [131, 134, 145, 146, 148, 287, 294, 302, 303, 309, 443, 449, 454, 462, 465, 587, 599, 606, 608, 614, 624, 638, 639, 642, 654] [132, 135, 146, 147, 149, 288, 295, 303, 304, 310, 444, 450, 455, 463, 466, 588, 600, 607, 609, 615, 625, 639, 640, 643, 655] [133, 136, 147, 148, 150, 289, 296, 304, 305, 311, 445, 451, 456, 464, 467, 589, 601, 608, 610, 616, 626, 640, 641, 644, 656] [134, 137, 148, 149, 151, 273, 290, 297, 305, 306, 429, 446, 452, 457, 465, 590, 602, 609, 611, 617, 627, 641, 642, 645, 657] [135, 138, 149, 150, 152, 274, 291, 298, 306, 307, 430, 447, 453, 458, 466, 591, 603, 610, 612, 618, 628, 642, 643, 646, 658] [136, 139, 150, 151, 153, 275, 292, 299, 307, 308, 431, 448, 454, 459, 467, 592, 604, 611, 613, 619, 629, 643, 644, 647, 659] [137, 140, 151, 152, 154, 276, 293, 300, 308, 309, 429, 432, 449, 455, 460, 593, 605, 612, 614, 620, 630, 644, 645, 648, 660] [138, 141, 152, 153, 155, 277, 294, 301, 309, 310, 430, 433, 450, 456, 461, 594, 606, 613, 615, 621, 631, 645, 646, 649, 661] [117, 139, 142, 153, 154, 278, 295, 302, 310, 311, 431, 434, 451, 457, 462, 595, 607, 614, 616, 622, 632, 646, 647, 650, 662] [118, 140, 143, 154, 155, 273, 279, 296, 303, 311, 432, 435, 452, 458, 463, 596, 608, 615, 617, 623, 624, 633, 647, 648, 651] [117, 119, 141, 144, 155, 273, 274, 280, 297, 304, 433, 436, 453, 459, 464, 585, 597, 609, 616, 618, 625, 634, 648, 649, 652] [117, 118, 120, 142, 145, 274, 275, 281, 298, 305, 434, 437, 454, 460, 465, 586, 598, 610, 617, 619, 626, 635, 649, 650, 653] [118, 119, 121, 143, 146, 275, 276, 282, 299, 306, 435, 438, 455, 461, 466, 587, 599, 611, 618, 620, 627, 636, 650, 651, 654] [119, 120, 122, 144, 147, 276, 277, 283, 300, 307, 436, 439, 456, 462, 467, 588, 600, 612, 619, 621, 628, 637, 651, 652, 655] [120, 121, 123, 145, 148, 277, 278, 284, 301, 308, 429, 437, 440, 457, 463, 589, 601, 613, 620, 622, 629, 638, 652, 653, 656] [121, 122, 124, 146, 149, 278, 279, 285, 302, 309, 430, 438, 441, 458, 464, 590, 602, 614, 621, 623, 630, 639, 653, 654, 657] [122, 123, 125, 147, 150, 279, 280, 286, 303, 310, 431, 439, 442, 459, 465, 585, 591, 603, 615, 622, 631, 640, 654, 655, 658] [123, 124, 126, 148, 151, 280, 281, 287, 304, 311, 432, 440, 443, 460, 466, 586, 592, 604, 616, 623, 632, 641, 655, 656, 659] [124, 125, 127, 149, 152, 273, 281, 282, 288, 305, 433, 441, 444, 461, 467, 585, 587, 593, 605, 617, 633, 642, 656, 657, 660] [125, 126, 128, 150, 153, 274, 282, 283, 289, 306, 429, 434, 442, 445, 462, 586, 588, 594, 606, 618, 634, 643, 657, 658, 661] [126, 127, 129, 151, 154, 275, 283, 284, 290, 307, 430, 435, 443, 446, 463, 587, 589, 595, 607, 619, 635, 644, 658, 659, 662] [127, 128, 130, 152, 155, 276, 284, 285, 291, 308, 431, 436, 444, 447, 464, 588, 590, 596, 608, 620, 624, 636, 645, 659, 660] [117, 128, 129, 131, 153, 277, 285, 286, 292, 309, 432, 437, 445, 448, 465, 589, 591, 597, 609, 621, 625, 637, 646, 660, 661] [118, 129, 130, 132, 154, 278, 286, 287, 293, 310, 433, 438, 446, 449, 466, 590, 592, 598, 610, 622, 626, 638, 647, 661, 662] [119, 130, 131, 133, 155, 279, 287, 288, 294, 311, 434, 439, 447, 450, 467, 591, 593, 599, 611, 623, 624, 627, 639, 648, 662]
H_Z (156 checks, sparse supports)
[0, 22, 28, 33, 37, 39, 55, 65, 72, 77, 78, 94, 103, 108, 115, 117, 131, 140, 152, 155, 624, 646, 648, 649, 660] [1, 23, 29, 34, 38, 39, 40, 56, 66, 73, 79, 95, 104, 109, 116, 117, 118, 132, 141, 153, 625, 647, 649, 650, 661] [0, 2, 24, 30, 35, 40, 41, 57, 67, 74, 78, 80, 96, 105, 110, 118, 119, 133, 142, 154, 626, 648, 650, 651, 662] [1, 3, 25, 31, 36, 41, 42, 58, 68, 75, 79, 81, 97, 106, 111, 119, 120, 134, 143, 155, 624, 627, 649, 651, 652] [2, 4, 26, 32, 37, 42, 43, 59, 69, 76, 80, 82, 98, 107, 112, 117, 120, 121, 135, 144, 625, 628, 650, 652, 653] [3, 5, 27, 33, 38, 43, 44, 60, 70, 77, 81, 83, 99, 108, 113, 118, 121, 122, 136, 145, 626, 629, 651, 653, 654] [0, 4, 6, 28, 34, 39, 44, 45, 61, 71, 82, 84, 100, 109, 114, 119, 122, 123, 137, 146, 627, 630, 652, 654, 655] [1, 5, 7, 29, 35, 40, 45, 46, 62, 72, 83, 85, 101, 110, 115, 120, 123, 124, 138, 147, 628, 631, 653, 655, 656] [2, 6, 8, 30, 36, 41, 46, 47, 63, 73, 84, 86, 102, 111, 116, 121, 124, 125, 139, 148, 629, 632, 654, 656, 657] [3, 7, 9, 31, 37, 42, 47, 48, 64, 74, 78, 85, 87, 103, 112, 122, 125, 126, 140, 149, 630, 633, 655, 657, 658] [4, 8, 10, 32, 38, 43, 48, 49, 65, 75, 79, 86, 88, 104, 113, 123, 126, 127, 141, 150, 631, 634, 656, 658, 659] [0, 5, 9, 11, 33, 44, 49, 50, 66, 76, 80, 87, 89, 105, 114, 124, 127, 128, 142, 151, 632, 635, 657, 659, 660] [1, 6, 10, 12, 34, 45, 50, 51, 67, 77, 81, 88, 90, 106, 115, 125, 128, 129, 143, 152, 633, 636, 658, 660, 661] [2, 7, 11, 13, 35, 39, 46, 51, 52, 68, 82, 89, 91, 107, 116, 126, 129, 130, 144, 153, 634, 637, 659, 661, 662] [3, 8, 12, 14, 36, 40, 47, 52, 53, 69, 78, 83, 90, 92, 108, 127, 130, 131, 145, 154, 624, 635, 638, 660, 662] [4, 9, 13, 15, 37, 41, 48, 53, 54, 70, 79, 84, 91, 93, 109, 128, 131, 132, 146, 155, 624, 625, 636, 639, 661] [5, 10, 14, 16, 38, 42, 49, 54, 55, 71, 80, 85, 92, 94, 110, 117, 129, 132, 133, 147, 625, 626, 637, 640, 662] [0, 6, 11, 15, 17, 43, 50, 55, 56, 72, 81, 86, 93, 95, 111, 118, 130, 133, 134, 148, 624, 626, 627, 638, 641] [1, 7, 12, 16, 18, 44, 51, 56, 57, 73, 82, 87, 94, 96, 112, 119, 131, 134, 135, 149, 625, 627, 628, 639, 642] [2, 8, 13, 17, 19, 45, 52, 57, 58, 74, 83, 88, 95, 97, 113, 120, 132, 135, 136, 150, 626, 628, 629, 640, 643] [3, 9, 14, 18, 20, 46, 53, 58, 59, 75, 84, 89, 96, 98, 114, 121, 133, 136, 137, 151, 627, 629, 630, 641, 644] [4, 10, 15, 19, 21, 47, 54, 59, 60, 76, 85, 90, 97, 99, 115, 122, 134, 137, 138, 152, 628, 630, 631, 642, 645] [5, 11, 16, 20, 22, 48, 55, 60, 61, 77, 86, 91, 98, 100, 116, 123, 135, 138, 139, 153, 629, 631, 632, 643, 646] [6, 12, 17, 21, 23, 39, 49, 56, 61, 62, 78, 87, 92, 99, 101, 124, 136, 139, 140, 154, 630, 632, 633, 644, 647] [7, 13, 18, 22, 24, 40, 50, 57, 62, 63, 79, 88, 93, 100, 102, 125, 137, 140, 141, 155, 631, 633, 634, 645, 648] [8, 14, 19, 23, 25, 41, 51, 58, 63, 64, 80, 89, 94, 101, 103, 117, 126, 138, 141, 142, 632, 634, 635, 646, 649] [9, 15, 20, 24, 26, 42, 52, 59, 64, 65, 81, 90, 95, 102, 104, 118, 127, 139, 142, 143, 633, 635, 636, 647, 650] [10, 16, 21, 25, 27, 43, 53, 60, 65, 66, 82, 91, 96, 103, 105, 119, 128, 140, 143, 144, 634, 636, 637, 648, 651] [11, 17, 22, 26, 28, 44, 54, 61, 66, 67, 83, 92, 97, 104, 106, 120, 129, 141, 144, 145, 635, 637, 638, 649, 652] [12, 18, 23, 27, 29, 45, 55, 62, 67, 68, 84, 93, 98, 105, 107, 121, 130, 142, 145, 146, 636, 638, 639, 650, 653] [13, 19, 24, 28, 30, 46, 56, 63, 68, 69, 85, 94, 99, 106, 108, 122, 131, 143, 146, 147, 637, 639, 640, 651, 654] [14, 20, 25, 29, 31, 47, 57, 64, 69, 70, 86, 95, 100, 107, 109, 123, 132, 144, 147, 148, 638, 640, 641, 652, 655] [15, 21, 26, 30, 32, 48, 58, 65, 70, 71, 87, 96, 101, 108, 110, 124, 133, 145, 148, 149, 639, 641, 642, 653, 656] [16, 22, 27, 31, 33, 49, 59, 66, 71, 72, 88, 97, 102, 109, 111, 125, 134, 146, 149, 150, 640, 642, 643, 654, 657] [17, 23, 28, 32, 34, 50, 60, 67, 72, 73, 89, 98, 103, 110, 112, 126, 135, 147, 150, 151, 641, 643, 644, 655, 658] [18, 24, 29, 33, 35, 51, 61, 68, 73, 74, 90, 99, 104, 111, 113, 127, 136, 148, 151, 152, 642, 644, 645, 656, 659] [19, 25, 30, 34, 36, 52, 62, 69, 74, 75, 91, 100, 105, 112, 114, 128, 137, 149, 152, 153, 643, 645, 646, 657, 660] [20, 26, 31, 35, 37, 53, 63, 70, 75, 76, 92, 101, 106, 113, 115, 129, 138, 150, 153, 154, 644, 646, 647, 658, 661] [21, 27, 32, 36, 38, 54, 64, 71, 76, 77, 93, 102, 107, 114, 116, 130, 139, 151, 154, 155, 645, 647, 648, 659, 662] [156, 178, 184, 189, 193, 195, 211, 221, 228, 233, 234, 250, 259, 264, 271, 273, 287, 296, 308, 311, 624, 641, 647, 648, 656] [157, 179, 185, 190, 194, 195, 196, 212, 222, 229, 235, 251, 260, 265, 272, 273, 274, 288, 297, 309, 625, 642, 648, 649, 657] [156, 158, 180, 186, 191, 196, 197, 213, 223, 230, 234, 236, 252, 261, 266, 274, 275, 289, 298, 310, 626, 643, 649, 650, 658] [157, 159, 181, 187, 192, 197, 198, 214, 224, 231, 235, 237, 253, 262, 267, 275, 276, 290, 299, 311, 627, 644, 650, 651, 659] [158, 160, 182, 188, 193, 198, 199, 215, 225, 232, 236, 238, 254, 263, 268, 273, 276, 277, 291, 300, 628, 645, 651, 652, 660] [159, 161, 183, 189, 194, 199, 200, 216, 226, 233, 237, 239, 255, 264, 269, 274, 277, 278, 292, 301, 629, 646, 652, 653, 661] [156, 160, 162, 184, 190, 195, 200, 201, 217, 227, 238, 240, 256, 265, 270, 275, 278, 279, 293, 302, 630, 647, 653, 654, 662] [157, 161, 163, 185, 191, 196, 201, 202, 218, 228, 239, 241, 257, 266, 271, 276, 279, 280, 294, 303, 624, 631, 648, 654, 655] [158, 162, 164, 186, 192, 197, 202, 203, 219, 229, 240, 242, 258, 267, 272, 277, 280, 281, 295, 304, 625, 632, 649, 655, 656] [159, 163, 165, 187, 193, 198, 203, 204, 220, 230, 234, 241, 243, 259, 268, 278, 281, 282, 296, 305, 626, 633, 650, 656, 657] [160, 164, 166, 188, 194, 199, 204, 205, 221, 231, 235, 242, 244, 260, 269, 279, 282, 283, 297, 306, 627, 634, 651, 657, 658] [156, 161, 165, 167, 189, 200, 205, 206, 222, 232, 236, 243, 245, 261, 270, 280, 283, 284, 298, 307, 628, 635, 652, 658, 659] [157, 162, 166, 168, 190, 201, 206, 207, 223, 233, 237, 244, 246, 262, 271, 281, 284, 285, 299, 308, 629, 636, 653, 659, 660] [158, 163, 167, 169, 191, 195, 202, 207, 208, 224, 238, 245, 247, 263, 272, 282, 285, 286, 300, 309, 630, 637, 654, 660, 661] [159, 164, 168, 170, 192, 196, 203, 208, 209, 225, 234, 239, 246, 248, 264, 283, 286, 287, 301, 310, 631, 638, 655, 661, 662] [160, 165, 169, 171, 193, 197, 204, 209, 210, 226, 235, 240, 247, 249, 265, 284, 287, 288, 302, 311, 624, 632, 639, 656, 662] [161, 166, 170, 172, 194, 198, 205, 210, 211, 227, 236, 241, 248, 250, 266, 273, 285, 288, 289, 303, 624, 625, 633, 640, 657] [156, 162, 167, 171, 173, 199, 206, 211, 212, 228, 237, 242, 249, 251, 267, 274, 286, 289, 290, 304, 625, 626, 634, 641, 658] [157, 163, 168, 172, 174, 200, 207, 212, 213, 229, 238, 243, 250, 252, 268, 275, 287, 290, 291, 305, 626, 627, 635, 642, 659] [158, 164, 169, 173, 175, 201, 208, 213, 214, 230, 239, 244, 251, 253, 269, 276, 288, 291, 292, 306, 627, 628, 636, 643, 660] [159, 165, 170, 174, 176, 202, 209, 214, 215, 231, 240, 245, 252, 254, 270, 277, 289, 292, 293, 307, 628, 629, 637, 644, 661] [160, 166, 171, 175, 177, 203, 210, 215, 216, 232, 241, 246, 253, 255, 271, 278, 290, 293, 294, 308, 629, 630, 638, 645, 662] [161, 167, 172, 176, 178, 204, 211, 216, 217, 233, 242, 247, 254, 256, 272, 279, 291, 294, 295, 309, 624, 630, 631, 639, 646] [162, 168, 173, 177, 179, 195, 205, 212, 217, 218, 234, 243, 248, 255, 257, 280, 292, 295, 296, 310, 625, 631, 632, 640, 647] [163, 169, 174, 178, 180, 196, 206, 213, 218, 219, 235, 244, 249, 256, 258, 281, 293, 296, 297, 311, 626, 632, 633, 641, 648] [164, 170, 175, 179, 181, 197, 207, 214, 219, 220, 236, 245, 250, 257, 259, 273, 282, 294, 297, 298, 627, 633, 634, 642, 649] [165, 171, 176, 180, 182, 198, 208, 215, 220, 221, 237, 246, 251, 258, 260, 274, 283, 295, 298, 299, 628, 634, 635, 643, 650] [166, 172, 177, 181, 183, 199, 209, 216, 221, 222, 238, 247, 252, 259, 261, 275, 284, 296, 299, 300, 629, 635, 636, 644, 651] [167, 173, 178, 182, 184, 200, 210, 217, 222, 223, 239, 248, 253, 260, 262, 276, 285, 297, 300, 301, 630, 636, 637, 645, 652] [168, 174, 179, 183, 185, 201, 211, 218, 223, 224, 240, 249, 254, 261, 263, 277, 286, 298, 301, 302, 631, 637, 638, 646, 653] [169, 175, 180, 184, 186, 202, 212, 219, 224, 225, 241, 250, 255, 262, 264, 278, 287, 299, 302, 303, 632, 638, 639, 647, 654] [170, 176, 181, 185, 187, 203, 213, 220, 225, 226, 242, 251, 256, 263, 265, 279, 288, 300, 303, 304, 633, 639, 640, 648, 655] [171, 177, 182, 186, 188, 204, 214, 221, 226, 227, 243, 252, 257, 264, 266, 280, 289, 301, 304, 305, 634, 640, 641, 649, 656] [172, 178, 183, 187, 189, 205, 215, 222, 227, 228, 244, 253, 258, 265, 267, 281, 290, 302, 305, 306, 635, 641, 642, 650, 657] [173, 179, 184, 188, 190, 206, 216, 223, 228, 229, 245, 254, 259, 266, 268, 282, 291, 303, 306, 307, 636, 642, 643, 651, 658] [174, 180, 185, 189, 191, 207, 217, 224, 229, 230, 246, 255, 260, 267, 269, 283, 292, 304, 307, 308, 637, 643, 644, 652, 659] [175, 181, 186, 190, 192, 208, 218, 225, 230, 231, 247, 256, 261, 268, 270, 284, 293, 305, 308, 309, 638, 644, 645, 653, 660] [176, 182, 187, 191, 193, 209, 219, 226, 231, 232, 248, 257, 262, 269, 271, 285, 294, 306, 309, 310, 639, 645, 646, 654, 661] [177, 183, 188, 192, 194, 210, 220, 227, 232, 233, 249, 258, 263, 270, 272, 286, 295, 307, 310, 311, 640, 646, 647, 655, 662] [312, 334, 340, 345, 349, 351, 367, 377, 384, 389, 390, 406, 415, 420, 427, 429, 443, 452, 464, 467, 624, 641, 644, 652, 657] [313, 335, 341, 346, 350, 351, 352, 368, 378, 385, 391, 407, 416, 421, 428, 429, 430, 444, 453, 465, 625, 642, 645, 653, 658] [312, 314, 336, 342, 347, 352, 353, 369, 379, 386, 390, 392, 408, 417, 422, 430, 431, 445, 454, 466, 626, 643, 646, 654, 659] [313, 315, 337, 343, 348, 353, 354, 370, 380, 387, 391, 393, 409, 418, 423, 431, 432, 446, 455, 467, 627, 644, 647, 655, 660] [314, 316, 338, 344, 349, 354, 355, 371, 381, 388, 392, 394, 410, 419, 424, 429, 432, 433, 447, 456, 628, 645, 648, 656, 661] [315, 317, 339, 345, 350, 355, 356, 372, 382, 389, 393, 395, 411, 420, 425, 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Code ID 663-351-10 · download JSON · raw on GitHub