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[[646,350,8]] d ≤
n
646
k
350
d
8
kd²/n
34.675
w
20
X/Z
1

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Distance

X/Z asymmetry 1 · d_X ≤ 8, d_Z ≤ 8 · w_X = 20, w_Z = 20 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)
d_X 8 · witness weight 8 (claimed upper_bound)
witness operator (support, 8 qubits)
[0, 1, 16, 20, 38, 40, 44, 53]
d_Z 8 · witness weight 8 (claimed upper_bound)
witness operator (support, 8 qubits)
[0, 22, 32, 33, 152, 184, 188, 189]
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 20 · H_Z 20
qubit degrees H_X 3–16 (mean 4.582) · H_Z 3–16 (mean 4.582)
trapping sets H_X (1,3)×64 (2,3)×272 (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
(1,3): 64 (1,4): 544 (1,12): 1 (1,14): 3 (1,15): 6 (1,16): 28 (2,3): 272 (2,4): 2312 (2,5): 2064 (2,6): 10664 (2,11): 1 (2,12): 12 (2,13): 26 (2,14): 252 (2,15): 220 (2,16): 1310 (2,17): 1524 (2,18): 5082 (2,22): 1 (2,23): 3 (2,24): 19 (2,25): 20 (2,26): 82 (2,27): 61 (2,28): 150 (2,29): 62 (2,30): 144
trapping sets H_Z (1,3)×64 (2,3)×184 (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
(1,3): 64 (1,4): 544 (1,12): 1 (1,14): 3 (1,15): 6 (1,16): 28 (2,3): 184 (2,4): 1564 (2,5): 2328 (2,6): 12028 (2,11): 1 (2,12): 11 (2,13): 29 (2,14): 252 (2,15): 220 (2,16): 1297 (2,17): 1543 (2,18): 5074 (2,20): 1 (2,22): 10 (2,23): 15 (2,24): 42 (2,25): 16 (2,26): 56 (2,27): 54 (2,28): 129 (2,29): 45 (2,30): 101

Construction & provenance

authors @hirobumii
provenance submitted through the challenge
novelty novelty not audited
construction C38 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, 1, 2, 6], [0, 5, 6, 16], [0, 1, 17, 19], [0, 9, 19, 21]]; B supports=[[0, 2, 6, 15], [0, 1, 16, 20], [0, 6, 17, 20], [0, 9, 17, 23]]. Every entry has rank37 with all-ones-only kernel. The sole row relation in each38-row block is its full sum. Selected rows omit X shifts[37, 37, 37, 37] and Z shifts[37, 37, 37, 37].
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 20, maximum qubit degree 32, 296 checks and total incidence 5920.
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

[[646,350,8]] - CSS sparse stabilizer code

Direction & hypothesis

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

What was searched

C38 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, 1, 2, 6], [0, 5, 6, 16], [0, 1, 17, 19], [0, 9, 19, 21]]; B supports=[[0, 2, 6, 15], [0, 1, 16, 20], [0, 6, 17, 20], [0, 9, 17, 23]]. Every entry has rank37 with all-ones-only kernel. The sole row relation in each38-row block is its full sum. Selected rows omit X shifts[37, 37, 37, 37] and Z shifts[37, 37, 37, 37].

The displayed presentation has maximum check weight 20, maximum qubit degree 32, 296 checks and total incidence 5920.

Evidence trail

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