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[[680,360,10]] d ≤
n
680
k
360
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, 6, 19, 23, 24, 40, 42, 45, 49, 51]
d_Z 10 · witness weight 10 (claimed upper_bound)
witness operator (support, 10 qubits)
[0, 18, 24, 25, 33, 160, 183, 185, 186, 197]
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)×640 (2,4)×320 (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): 640 (1,20): 40 (2,4): 320 (2,6): 4720 (2,8): 20000 (2,19): 200 (2,21): 2280 (2,23): 10840 (2,32): 80 (2,34): 240 (2,36): 220 (2,38): 120
trapping sets H_Z (1,5)×640 (2,4)×320 (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): 640 (1,20): 40 (2,4): 320 (2,6): 4720 (2,8): 20000 (2,19): 200 (2,21): 2280 (2,23): 10840 (2,32): 80 (2,34): 240 (2,36): 220 (2,38): 120

Construction & provenance

authors @hirobumii
provenance submitted through the challenge
novelty novelty not audited
construction C40 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, 12, 19, 21, 27], [0, 8, 11, 19, 28]]; B supports=[[0, 2, 5, 9, 11], [0, 6, 19, 23, 24], [0, 5, 8, 21, 26], [0, 7, 16, 23, 27]]. 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, 320 checks and total incidence 8000.
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

[[680,360,10]] - CSS sparse stabilizer code

Direction & hypothesis

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

What was searched

C40 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, 12, 19, 21, 27], [0, 8, 11, 19, 28]]; B supports=[[0, 2, 5, 9, 11], [0, 6, 19, 23, 24], [0, 5, 8, 21, 26], [0, 7, 16, 23, 27]]. Every individual entry is invertible.

The displayed presentation has maximum check weight 25, maximum qubit degree 40, 320 checks and total incidence 8000.

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/680-360-10.json. Allocate zero binary matrices H_X and H_Z with 680 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 160 (max weight 25) · Z-checks 160 (max weight 25)
H_X (160 checks, sparse supports)
[0, 3, 14, 15, 17, 160, 167, 175, 176, 182, 320, 332, 339, 341, 347, 480, 488, 491, 499, 508, 640, 642, 645, 649, 651] [1, 4, 15, 16, 18, 161, 168, 176, 177, 183, 321, 333, 340, 342, 348, 481, 489, 492, 500, 509, 641, 643, 646, 650, 652] [2, 5, 16, 17, 19, 162, 169, 177, 178, 184, 322, 334, 341, 343, 349, 482, 490, 493, 501, 510, 642, 644, 647, 651, 653] [3, 6, 17, 18, 20, 163, 170, 178, 179, 185, 323, 335, 342, 344, 350, 483, 491, 494, 502, 511, 643, 645, 648, 652, 654] [4, 7, 18, 19, 21, 164, 171, 179, 180, 186, 324, 336, 343, 345, 351, 484, 492, 495, 503, 512, 644, 646, 649, 653, 655] [5, 8, 19, 20, 22, 165, 172, 180, 181, 187, 325, 337, 344, 346, 352, 485, 493, 496, 504, 513, 645, 647, 650, 654, 656] [6, 9, 20, 21, 23, 166, 173, 181, 182, 188, 326, 338, 345, 347, 353, 486, 494, 497, 505, 514, 646, 648, 651, 655, 657] [7, 10, 21, 22, 24, 167, 174, 182, 183, 189, 327, 339, 346, 348, 354, 487, 495, 498, 506, 515, 647, 649, 652, 656, 658] [8, 11, 22, 23, 25, 168, 175, 183, 184, 190, 328, 340, 347, 349, 355, 488, 496, 499, 507, 516, 648, 650, 653, 657, 659] [9, 12, 23, 24, 26, 169, 176, 184, 185, 191, 329, 341, 348, 350, 356, 489, 497, 500, 508, 517, 649, 651, 654, 658, 660] [10, 13, 24, 25, 27, 170, 177, 185, 186, 192, 330, 342, 349, 351, 357, 490, 498, 501, 509, 518, 650, 652, 655, 659, 661] [11, 14, 25, 26, 28, 171, 178, 186, 187, 193, 331, 343, 350, 352, 358, 491, 499, 502, 510, 519, 651, 653, 656, 660, 662] [12, 15, 26, 27, 29, 172, 179, 187, 188, 194, 332, 344, 351, 353, 359, 480, 492, 500, 503, 511, 652, 654, 657, 661, 663] [13, 16, 27, 28, 30, 173, 180, 188, 189, 195, 320, 333, 345, 352, 354, 481, 493, 501, 504, 512, 653, 655, 658, 662, 664] [14, 17, 28, 29, 31, 174, 181, 189, 190, 196, 321, 334, 346, 353, 355, 482, 494, 502, 505, 513, 654, 656, 659, 663, 665] [15, 18, 29, 30, 32, 175, 182, 190, 191, 197, 322, 335, 347, 354, 356, 483, 495, 503, 506, 514, 655, 657, 660, 664, 666] [16, 19, 30, 31, 33, 176, 183, 191, 192, 198, 323, 336, 348, 355, 357, 484, 496, 504, 507, 515, 656, 658, 661, 665, 667] [17, 20, 31, 32, 34, 177, 184, 192, 193, 199, 324, 337, 349, 356, 358, 485, 497, 505, 508, 516, 657, 659, 662, 666, 668] [18, 21, 32, 33, 35, 160, 178, 185, 193, 194, 325, 338, 350, 357, 359, 486, 498, 506, 509, 517, 658, 660, 663, 667, 669] [19, 22, 33, 34, 36, 161, 179, 186, 194, 195, 320, 326, 339, 351, 358, 487, 499, 507, 510, 518, 659, 661, 664, 668, 670] [20, 23, 34, 35, 37, 162, 180, 187, 195, 196, 321, 327, 340, 352, 359, 488, 500, 508, 511, 519, 660, 662, 665, 669, 671] [21, 24, 35, 36, 38, 163, 181, 188, 196, 197, 320, 322, 328, 341, 353, 480, 489, 501, 509, 512, 661, 663, 666, 670, 672] [22, 25, 36, 37, 39, 164, 182, 189, 197, 198, 321, 323, 329, 342, 354, 481, 490, 502, 510, 513, 662, 664, 667, 671, 673] [0, 23, 26, 37, 38, 165, 183, 190, 198, 199, 322, 324, 330, 343, 355, 482, 491, 503, 511, 514, 663, 665, 668, 672, 674] [1, 24, 27, 38, 39, 160, 166, 184, 191, 199, 323, 325, 331, 344, 356, 483, 492, 504, 512, 515, 664, 666, 669, 673, 675] [0, 2, 25, 28, 39, 160, 161, 167, 185, 192, 324, 326, 332, 345, 357, 484, 493, 505, 513, 516, 665, 667, 670, 674, 676] [0, 1, 3, 26, 29, 161, 162, 168, 186, 193, 325, 327, 333, 346, 358, 485, 494, 506, 514, 517, 666, 668, 671, 675, 677] [1, 2, 4, 27, 30, 162, 163, 169, 187, 194, 326, 328, 334, 347, 359, 486, 495, 507, 515, 518, 667, 669, 672, 676, 678] [2, 3, 5, 28, 31, 163, 164, 170, 188, 195, 320, 327, 329, 335, 348, 487, 496, 508, 516, 519, 668, 670, 673, 677, 679] [3, 4, 6, 29, 32, 164, 165, 171, 189, 196, 321, 328, 330, 336, 349, 480, 488, 497, 509, 517, 640, 669, 671, 674, 678] [4, 5, 7, 30, 33, 165, 166, 172, 190, 197, 322, 329, 331, 337, 350, 481, 489, 498, 510, 518, 641, 670, 672, 675, 679] [5, 6, 8, 31, 34, 166, 167, 173, 191, 198, 323, 330, 332, 338, 351, 482, 490, 499, 511, 519, 640, 642, 671, 673, 676] [6, 7, 9, 32, 35, 167, 168, 174, 192, 199, 324, 331, 333, 339, 352, 480, 483, 491, 500, 512, 641, 643, 672, 674, 677] [7, 8, 10, 33, 36, 160, 168, 169, 175, 193, 325, 332, 334, 340, 353, 481, 484, 492, 501, 513, 642, 644, 673, 675, 678] [8, 9, 11, 34, 37, 161, 169, 170, 176, 194, 326, 333, 335, 341, 354, 482, 485, 493, 502, 514, 643, 645, 674, 676, 679] [9, 10, 12, 35, 38, 162, 170, 171, 177, 195, 327, 334, 336, 342, 355, 483, 486, 494, 503, 515, 640, 644, 646, 675, 677] [10, 11, 13, 36, 39, 163, 171, 172, 178, 196, 328, 335, 337, 343, 356, 484, 487, 495, 504, 516, 641, 645, 647, 676, 678] [0, 11, 12, 14, 37, 164, 172, 173, 179, 197, 329, 336, 338, 344, 357, 485, 488, 496, 505, 517, 642, 646, 648, 677, 679] [1, 12, 13, 15, 38, 165, 173, 174, 180, 198, 330, 337, 339, 345, 358, 486, 489, 497, 506, 518, 640, 643, 647, 649, 678] [2, 13, 14, 16, 39, 166, 174, 175, 181, 199, 331, 338, 340, 346, 359, 487, 490, 498, 507, 519, 641, 644, 648, 650, 679] [40, 43, 54, 55, 57, 200, 207, 215, 216, 222, 360, 372, 379, 381, 387, 520, 528, 531, 539, 548, 640, 646, 659, 663, 664] [41, 44, 55, 56, 58, 201, 208, 216, 217, 223, 361, 373, 380, 382, 388, 521, 529, 532, 540, 549, 641, 647, 660, 664, 665] [42, 45, 56, 57, 59, 202, 209, 217, 218, 224, 362, 374, 381, 383, 389, 522, 530, 533, 541, 550, 642, 648, 661, 665, 666] [43, 46, 57, 58, 60, 203, 210, 218, 219, 225, 363, 375, 382, 384, 390, 523, 531, 534, 542, 551, 643, 649, 662, 666, 667] [44, 47, 58, 59, 61, 204, 211, 219, 220, 226, 364, 376, 383, 385, 391, 524, 532, 535, 543, 552, 644, 650, 663, 667, 668] [45, 48, 59, 60, 62, 205, 212, 220, 221, 227, 365, 377, 384, 386, 392, 525, 533, 536, 544, 553, 645, 651, 664, 668, 669] [46, 49, 60, 61, 63, 206, 213, 221, 222, 228, 366, 378, 385, 387, 393, 526, 534, 537, 545, 554, 646, 652, 665, 669, 670] [47, 50, 61, 62, 64, 207, 214, 222, 223, 229, 367, 379, 386, 388, 394, 527, 535, 538, 546, 555, 647, 653, 666, 670, 671] [48, 51, 62, 63, 65, 208, 215, 223, 224, 230, 368, 380, 387, 389, 395, 528, 536, 539, 547, 556, 648, 654, 667, 671, 672] [49, 52, 63, 64, 66, 209, 216, 224, 225, 231, 369, 381, 388, 390, 396, 529, 537, 540, 548, 557, 649, 655, 668, 672, 673] [50, 53, 64, 65, 67, 210, 217, 225, 226, 232, 370, 382, 389, 391, 397, 530, 538, 541, 549, 558, 650, 656, 669, 673, 674] [51, 54, 65, 66, 68, 211, 218, 226, 227, 233, 371, 383, 390, 392, 398, 531, 539, 542, 550, 559, 651, 657, 670, 674, 675] [52, 55, 66, 67, 69, 212, 219, 227, 228, 234, 372, 384, 391, 393, 399, 520, 532, 540, 543, 551, 652, 658, 671, 675, 676] [53, 56, 67, 68, 70, 213, 220, 228, 229, 235, 360, 373, 385, 392, 394, 521, 533, 541, 544, 552, 653, 659, 672, 676, 677] [54, 57, 68, 69, 71, 214, 221, 229, 230, 236, 361, 374, 386, 393, 395, 522, 534, 542, 545, 553, 654, 660, 673, 677, 678] [55, 58, 69, 70, 72, 215, 222, 230, 231, 237, 362, 375, 387, 394, 396, 523, 535, 543, 546, 554, 655, 661, 674, 678, 679] [56, 59, 70, 71, 73, 216, 223, 231, 232, 238, 363, 376, 388, 395, 397, 524, 536, 544, 547, 555, 640, 656, 662, 675, 679] [57, 60, 71, 72, 74, 217, 224, 232, 233, 239, 364, 377, 389, 396, 398, 525, 537, 545, 548, 556, 640, 641, 657, 663, 676] [58, 61, 72, 73, 75, 200, 218, 225, 233, 234, 365, 378, 390, 397, 399, 526, 538, 546, 549, 557, 641, 642, 658, 664, 677] [59, 62, 73, 74, 76, 201, 219, 226, 234, 235, 360, 366, 379, 391, 398, 527, 539, 547, 550, 558, 642, 643, 659, 665, 678] [60, 63, 74, 75, 77, 202, 220, 227, 235, 236, 361, 367, 380, 392, 399, 528, 540, 548, 551, 559, 643, 644, 660, 666, 679] [61, 64, 75, 76, 78, 203, 221, 228, 236, 237, 360, 362, 368, 381, 393, 520, 529, 541, 549, 552, 640, 644, 645, 661, 667] [62, 65, 76, 77, 79, 204, 222, 229, 237, 238, 361, 363, 369, 382, 394, 521, 530, 542, 550, 553, 641, 645, 646, 662, 668] [40, 63, 66, 77, 78, 205, 223, 230, 238, 239, 362, 364, 370, 383, 395, 522, 531, 543, 551, 554, 642, 646, 647, 663, 669] [41, 64, 67, 78, 79, 200, 206, 224, 231, 239, 363, 365, 371, 384, 396, 523, 532, 544, 552, 555, 643, 647, 648, 664, 670] [40, 42, 65, 68, 79, 200, 201, 207, 225, 232, 364, 366, 372, 385, 397, 524, 533, 545, 553, 556, 644, 648, 649, 665, 671] [40, 41, 43, 66, 69, 201, 202, 208, 226, 233, 365, 367, 373, 386, 398, 525, 534, 546, 554, 557, 645, 649, 650, 666, 672] [41, 42, 44, 67, 70, 202, 203, 209, 227, 234, 366, 368, 374, 387, 399, 526, 535, 547, 555, 558, 646, 650, 651, 667, 673] [42, 43, 45, 68, 71, 203, 204, 210, 228, 235, 360, 367, 369, 375, 388, 527, 536, 548, 556, 559, 647, 651, 652, 668, 674] [43, 44, 46, 69, 72, 204, 205, 211, 229, 236, 361, 368, 370, 376, 389, 520, 528, 537, 549, 557, 648, 652, 653, 669, 675] [44, 45, 47, 70, 73, 205, 206, 212, 230, 237, 362, 369, 371, 377, 390, 521, 529, 538, 550, 558, 649, 653, 654, 670, 676] [45, 46, 48, 71, 74, 206, 207, 213, 231, 238, 363, 370, 372, 378, 391, 522, 530, 539, 551, 559, 650, 654, 655, 671, 677] [46, 47, 49, 72, 75, 207, 208, 214, 232, 239, 364, 371, 373, 379, 392, 520, 523, 531, 540, 552, 651, 655, 656, 672, 678] [47, 48, 50, 73, 76, 200, 208, 209, 215, 233, 365, 372, 374, 380, 393, 521, 524, 532, 541, 553, 652, 656, 657, 673, 679] [48, 49, 51, 74, 77, 201, 209, 210, 216, 234, 366, 373, 375, 381, 394, 522, 525, 533, 542, 554, 640, 653, 657, 658, 674] [49, 50, 52, 75, 78, 202, 210, 211, 217, 235, 367, 374, 376, 382, 395, 523, 526, 534, 543, 555, 641, 654, 658, 659, 675] [50, 51, 53, 76, 79, 203, 211, 212, 218, 236, 368, 375, 377, 383, 396, 524, 527, 535, 544, 556, 642, 655, 659, 660, 676] [40, 51, 52, 54, 77, 204, 212, 213, 219, 237, 369, 376, 378, 384, 397, 525, 528, 536, 545, 557, 643, 656, 660, 661, 677] [41, 52, 53, 55, 78, 205, 213, 214, 220, 238, 370, 377, 379, 385, 398, 526, 529, 537, 546, 558, 644, 657, 661, 662, 678] [42, 53, 54, 56, 79, 206, 214, 215, 221, 239, 371, 378, 380, 386, 399, 527, 530, 538, 547, 559, 645, 658, 662, 663, 679] [80, 83, 94, 95, 97, 240, 247, 255, 256, 262, 400, 412, 419, 421, 427, 560, 568, 571, 579, 588, 640, 645, 648, 661, 666] [81, 84, 95, 96, 98, 241, 248, 256, 257, 263, 401, 413, 420, 422, 428, 561, 569, 572, 580, 589, 641, 646, 649, 662, 667] [82, 85, 96, 97, 99, 242, 249, 257, 258, 264, 402, 414, 421, 423, 429, 562, 570, 573, 581, 590, 642, 647, 650, 663, 668] [83, 86, 97, 98, 100, 243, 250, 258, 259, 265, 403, 415, 422, 424, 430, 563, 571, 574, 582, 591, 643, 648, 651, 664, 669] [84, 87, 98, 99, 101, 244, 251, 259, 260, 266, 404, 416, 423, 425, 431, 564, 572, 575, 583, 592, 644, 649, 652, 665, 670] [85, 88, 99, 100, 102, 245, 252, 260, 261, 267, 405, 417, 424, 426, 432, 565, 573, 576, 584, 593, 645, 650, 653, 666, 671] [86, 89, 100, 101, 103, 246, 253, 261, 262, 268, 406, 418, 425, 427, 433, 566, 574, 577, 585, 594, 646, 651, 654, 667, 672] [87, 90, 101, 102, 104, 247, 254, 262, 263, 269, 407, 419, 426, 428, 434, 567, 575, 578, 586, 595, 647, 652, 655, 668, 673] [88, 91, 102, 103, 105, 248, 255, 263, 264, 270, 408, 420, 427, 429, 435, 568, 576, 579, 587, 596, 648, 653, 656, 669, 674] [89, 92, 103, 104, 106, 249, 256, 264, 265, 271, 409, 421, 428, 430, 436, 569, 577, 580, 588, 597, 649, 654, 657, 670, 675] [90, 93, 104, 105, 107, 250, 257, 265, 266, 272, 410, 422, 429, 431, 437, 570, 578, 581, 589, 598, 650, 655, 658, 671, 676] [91, 94, 105, 106, 108, 251, 258, 266, 267, 273, 411, 423, 430, 432, 438, 571, 579, 582, 590, 599, 651, 656, 659, 672, 677] [92, 95, 106, 107, 109, 252, 259, 267, 268, 274, 412, 424, 431, 433, 439, 560, 572, 580, 583, 591, 652, 657, 660, 673, 678] [93, 96, 107, 108, 110, 253, 260, 268, 269, 275, 400, 413, 425, 432, 434, 561, 573, 581, 584, 592, 653, 658, 661, 674, 679] [94, 97, 108, 109, 111, 254, 261, 269, 270, 276, 401, 414, 426, 433, 435, 562, 574, 582, 585, 593, 640, 654, 659, 662, 675] [95, 98, 109, 110, 112, 255, 262, 270, 271, 277, 402, 415, 427, 434, 436, 563, 575, 583, 586, 594, 641, 655, 660, 663, 676] [96, 99, 110, 111, 113, 256, 263, 271, 272, 278, 403, 416, 428, 435, 437, 564, 576, 584, 587, 595, 642, 656, 661, 664, 677] [97, 100, 111, 112, 114, 257, 264, 272, 273, 279, 404, 417, 429, 436, 438, 565, 577, 585, 588, 596, 643, 657, 662, 665, 678] [98, 101, 112, 113, 115, 240, 258, 265, 273, 274, 405, 418, 430, 437, 439, 566, 578, 586, 589, 597, 644, 658, 663, 666, 679] [99, 102, 113, 114, 116, 241, 259, 266, 274, 275, 400, 406, 419, 431, 438, 567, 579, 587, 590, 598, 640, 645, 659, 664, 667] [100, 103, 114, 115, 117, 242, 260, 267, 275, 276, 401, 407, 420, 432, 439, 568, 580, 588, 591, 599, 641, 646, 660, 665, 668] [101, 104, 115, 116, 118, 243, 261, 268, 276, 277, 400, 402, 408, 421, 433, 560, 569, 581, 589, 592, 642, 647, 661, 666, 669] [102, 105, 116, 117, 119, 244, 262, 269, 277, 278, 401, 403, 409, 422, 434, 561, 570, 582, 590, 593, 643, 648, 662, 667, 670] [80, 103, 106, 117, 118, 245, 263, 270, 278, 279, 402, 404, 410, 423, 435, 562, 571, 583, 591, 594, 644, 649, 663, 668, 671] [81, 104, 107, 118, 119, 240, 246, 264, 271, 279, 403, 405, 411, 424, 436, 563, 572, 584, 592, 595, 645, 650, 664, 669, 672] [80, 82, 105, 108, 119, 240, 241, 247, 265, 272, 404, 406, 412, 425, 437, 564, 573, 585, 593, 596, 646, 651, 665, 670, 673] [80, 81, 83, 106, 109, 241, 242, 248, 266, 273, 405, 407, 413, 426, 438, 565, 574, 586, 594, 597, 647, 652, 666, 671, 674] [81, 82, 84, 107, 110, 242, 243, 249, 267, 274, 406, 408, 414, 427, 439, 566, 575, 587, 595, 598, 648, 653, 667, 672, 675] [82, 83, 85, 108, 111, 243, 244, 250, 268, 275, 400, 407, 409, 415, 428, 567, 576, 588, 596, 599, 649, 654, 668, 673, 676] [83, 84, 86, 109, 112, 244, 245, 251, 269, 276, 401, 408, 410, 416, 429, 560, 568, 577, 589, 597, 650, 655, 669, 674, 677] [84, 85, 87, 110, 113, 245, 246, 252, 270, 277, 402, 409, 411, 417, 430, 561, 569, 578, 590, 598, 651, 656, 670, 675, 678] [85, 86, 88, 111, 114, 246, 247, 253, 271, 278, 403, 410, 412, 418, 431, 562, 570, 579, 591, 599, 652, 657, 671, 676, 679] [86, 87, 89, 112, 115, 247, 248, 254, 272, 279, 404, 411, 413, 419, 432, 560, 563, 571, 580, 592, 640, 653, 658, 672, 677] [87, 88, 90, 113, 116, 240, 248, 249, 255, 273, 405, 412, 414, 420, 433, 561, 564, 572, 581, 593, 641, 654, 659, 673, 678] [88, 89, 91, 114, 117, 241, 249, 250, 256, 274, 406, 413, 415, 421, 434, 562, 565, 573, 582, 594, 642, 655, 660, 674, 679] [89, 90, 92, 115, 118, 242, 250, 251, 257, 275, 407, 414, 416, 422, 435, 563, 566, 574, 583, 595, 640, 643, 656, 661, 675] [90, 91, 93, 116, 119, 243, 251, 252, 258, 276, 408, 415, 417, 423, 436, 564, 567, 575, 584, 596, 641, 644, 657, 662, 676] [80, 91, 92, 94, 117, 244, 252, 253, 259, 277, 409, 416, 418, 424, 437, 565, 568, 576, 585, 597, 642, 645, 658, 663, 677] [81, 92, 93, 95, 118, 245, 253, 254, 260, 278, 410, 417, 419, 425, 438, 566, 569, 577, 586, 598, 643, 646, 659, 664, 678] [82, 93, 94, 96, 119, 246, 254, 255, 261, 279, 411, 418, 420, 426, 439, 567, 570, 578, 587, 599, 644, 647, 660, 665, 679] [120, 123, 134, 135, 137, 280, 287, 295, 296, 302, 440, 452, 459, 461, 467, 600, 608, 611, 619, 628, 640, 647, 656, 663, 667] [121, 124, 135, 136, 138, 281, 288, 296, 297, 303, 441, 453, 460, 462, 468, 601, 609, 612, 620, 629, 641, 648, 657, 664, 668] [122, 125, 136, 137, 139, 282, 289, 297, 298, 304, 442, 454, 461, 463, 469, 602, 610, 613, 621, 630, 642, 649, 658, 665, 669] [123, 126, 137, 138, 140, 283, 290, 298, 299, 305, 443, 455, 462, 464, 470, 603, 611, 614, 622, 631, 643, 650, 659, 666, 670] [124, 127, 138, 139, 141, 284, 291, 299, 300, 306, 444, 456, 463, 465, 471, 604, 612, 615, 623, 632, 644, 651, 660, 667, 671] [125, 128, 139, 140, 142, 285, 292, 300, 301, 307, 445, 457, 464, 466, 472, 605, 613, 616, 624, 633, 645, 652, 661, 668, 672] [126, 129, 140, 141, 143, 286, 293, 301, 302, 308, 446, 458, 465, 467, 473, 606, 614, 617, 625, 634, 646, 653, 662, 669, 673] [127, 130, 141, 142, 144, 287, 294, 302, 303, 309, 447, 459, 466, 468, 474, 607, 615, 618, 626, 635, 647, 654, 663, 670, 674] [128, 131, 142, 143, 145, 288, 295, 303, 304, 310, 448, 460, 467, 469, 475, 608, 616, 619, 627, 636, 648, 655, 664, 671, 675] [129, 132, 143, 144, 146, 289, 296, 304, 305, 311, 449, 461, 468, 470, 476, 609, 617, 620, 628, 637, 649, 656, 665, 672, 676] [130, 133, 144, 145, 147, 290, 297, 305, 306, 312, 450, 462, 469, 471, 477, 610, 618, 621, 629, 638, 650, 657, 666, 673, 677] [131, 134, 145, 146, 148, 291, 298, 306, 307, 313, 451, 463, 470, 472, 478, 611, 619, 622, 630, 639, 651, 658, 667, 674, 678] [132, 135, 146, 147, 149, 292, 299, 307, 308, 314, 452, 464, 471, 473, 479, 600, 612, 620, 623, 631, 652, 659, 668, 675, 679] [133, 136, 147, 148, 150, 293, 300, 308, 309, 315, 440, 453, 465, 472, 474, 601, 613, 621, 624, 632, 640, 653, 660, 669, 676] [134, 137, 148, 149, 151, 294, 301, 309, 310, 316, 441, 454, 466, 473, 475, 602, 614, 622, 625, 633, 641, 654, 661, 670, 677] [135, 138, 149, 150, 152, 295, 302, 310, 311, 317, 442, 455, 467, 474, 476, 603, 615, 623, 626, 634, 642, 655, 662, 671, 678] [136, 139, 150, 151, 153, 296, 303, 311, 312, 318, 443, 456, 468, 475, 477, 604, 616, 624, 627, 635, 643, 656, 663, 672, 679] [137, 140, 151, 152, 154, 297, 304, 312, 313, 319, 444, 457, 469, 476, 478, 605, 617, 625, 628, 636, 640, 644, 657, 664, 673] [138, 141, 152, 153, 155, 280, 298, 305, 313, 314, 445, 458, 470, 477, 479, 606, 618, 626, 629, 637, 641, 645, 658, 665, 674] [139, 142, 153, 154, 156, 281, 299, 306, 314, 315, 440, 446, 459, 471, 478, 607, 619, 627, 630, 638, 642, 646, 659, 666, 675] [140, 143, 154, 155, 157, 282, 300, 307, 315, 316, 441, 447, 460, 472, 479, 608, 620, 628, 631, 639, 643, 647, 660, 667, 676] [141, 144, 155, 156, 158, 283, 301, 308, 316, 317, 440, 442, 448, 461, 473, 600, 609, 621, 629, 632, 644, 648, 661, 668, 677] [142, 145, 156, 157, 159, 284, 302, 309, 317, 318, 441, 443, 449, 462, 474, 601, 610, 622, 630, 633, 645, 649, 662, 669, 678] [120, 143, 146, 157, 158, 285, 303, 310, 318, 319, 442, 444, 450, 463, 475, 602, 611, 623, 631, 634, 646, 650, 663, 670, 679] [121, 144, 147, 158, 159, 280, 286, 304, 311, 319, 443, 445, 451, 464, 476, 603, 612, 624, 632, 635, 640, 647, 651, 664, 671] [120, 122, 145, 148, 159, 280, 281, 287, 305, 312, 444, 446, 452, 465, 477, 604, 613, 625, 633, 636, 641, 648, 652, 665, 672] [120, 121, 123, 146, 149, 281, 282, 288, 306, 313, 445, 447, 453, 466, 478, 605, 614, 626, 634, 637, 642, 649, 653, 666, 673] [121, 122, 124, 147, 150, 282, 283, 289, 307, 314, 446, 448, 454, 467, 479, 606, 615, 627, 635, 638, 643, 650, 654, 667, 674] [122, 123, 125, 148, 151, 283, 284, 290, 308, 315, 440, 447, 449, 455, 468, 607, 616, 628, 636, 639, 644, 651, 655, 668, 675] [123, 124, 126, 149, 152, 284, 285, 291, 309, 316, 441, 448, 450, 456, 469, 600, 608, 617, 629, 637, 645, 652, 656, 669, 676] [124, 125, 127, 150, 153, 285, 286, 292, 310, 317, 442, 449, 451, 457, 470, 601, 609, 618, 630, 638, 646, 653, 657, 670, 677] [125, 126, 128, 151, 154, 286, 287, 293, 311, 318, 443, 450, 452, 458, 471, 602, 610, 619, 631, 639, 647, 654, 658, 671, 678] [126, 127, 129, 152, 155, 287, 288, 294, 312, 319, 444, 451, 453, 459, 472, 600, 603, 611, 620, 632, 648, 655, 659, 672, 679] [127, 128, 130, 153, 156, 280, 288, 289, 295, 313, 445, 452, 454, 460, 473, 601, 604, 612, 621, 633, 640, 649, 656, 660, 673] [128, 129, 131, 154, 157, 281, 289, 290, 296, 314, 446, 453, 455, 461, 474, 602, 605, 613, 622, 634, 641, 650, 657, 661, 674] [129, 130, 132, 155, 158, 282, 290, 291, 297, 315, 447, 454, 456, 462, 475, 603, 606, 614, 623, 635, 642, 651, 658, 662, 675] [130, 131, 133, 156, 159, 283, 291, 292, 298, 316, 448, 455, 457, 463, 476, 604, 607, 615, 624, 636, 643, 652, 659, 663, 676] [120, 131, 132, 134, 157, 284, 292, 293, 299, 317, 449, 456, 458, 464, 477, 605, 608, 616, 625, 637, 644, 653, 660, 664, 677] [121, 132, 133, 135, 158, 285, 293, 294, 300, 318, 450, 457, 459, 465, 478, 606, 609, 617, 626, 638, 645, 654, 661, 665, 678] [122, 133, 134, 136, 159, 286, 294, 295, 301, 319, 451, 458, 460, 466, 479, 607, 610, 618, 627, 639, 646, 655, 662, 666, 679]
H_Z (160 checks, sparse supports)
[0, 29, 31, 35, 38, 40, 56, 57, 61, 74, 80, 94, 99, 112, 115, 120, 133, 137, 144, 153, 640, 663, 665, 666, 677] [1, 30, 32, 36, 39, 41, 57, 58, 62, 75, 81, 95, 100, 113, 116, 121, 134, 138, 145, 154, 641, 664, 666, 667, 678] [0, 2, 31, 33, 37, 42, 58, 59, 63, 76, 82, 96, 101, 114, 117, 122, 135, 139, 146, 155, 642, 665, 667, 668, 679] [1, 3, 32, 34, 38, 43, 59, 60, 64, 77, 83, 97, 102, 115, 118, 123, 136, 140, 147, 156, 640, 643, 666, 668, 669] [2, 4, 33, 35, 39, 44, 60, 61, 65, 78, 84, 98, 103, 116, 119, 124, 137, 141, 148, 157, 641, 644, 667, 669, 670] [0, 3, 5, 34, 36, 45, 61, 62, 66, 79, 80, 85, 99, 104, 117, 125, 138, 142, 149, 158, 642, 645, 668, 670, 671] [1, 4, 6, 35, 37, 40, 46, 62, 63, 67, 81, 86, 100, 105, 118, 126, 139, 143, 150, 159, 643, 646, 669, 671, 672] [2, 5, 7, 36, 38, 41, 47, 63, 64, 68, 82, 87, 101, 106, 119, 120, 127, 140, 144, 151, 644, 647, 670, 672, 673] [3, 6, 8, 37, 39, 42, 48, 64, 65, 69, 80, 83, 88, 102, 107, 121, 128, 141, 145, 152, 645, 648, 671, 673, 674] [0, 4, 7, 9, 38, 43, 49, 65, 66, 70, 81, 84, 89, 103, 108, 122, 129, 142, 146, 153, 646, 649, 672, 674, 675] [1, 5, 8, 10, 39, 44, 50, 66, 67, 71, 82, 85, 90, 104, 109, 123, 130, 143, 147, 154, 647, 650, 673, 675, 676] [0, 2, 6, 9, 11, 45, 51, 67, 68, 72, 83, 86, 91, 105, 110, 124, 131, 144, 148, 155, 648, 651, 674, 676, 677] [1, 3, 7, 10, 12, 46, 52, 68, 69, 73, 84, 87, 92, 106, 111, 125, 132, 145, 149, 156, 649, 652, 675, 677, 678] [2, 4, 8, 11, 13, 47, 53, 69, 70, 74, 85, 88, 93, 107, 112, 126, 133, 146, 150, 157, 650, 653, 676, 678, 679] [3, 5, 9, 12, 14, 48, 54, 70, 71, 75, 86, 89, 94, 108, 113, 127, 134, 147, 151, 158, 640, 651, 654, 677, 679] [4, 6, 10, 13, 15, 49, 55, 71, 72, 76, 87, 90, 95, 109, 114, 128, 135, 148, 152, 159, 640, 641, 652, 655, 678] [5, 7, 11, 14, 16, 50, 56, 72, 73, 77, 88, 91, 96, 110, 115, 120, 129, 136, 149, 153, 641, 642, 653, 656, 679] [6, 8, 12, 15, 17, 51, 57, 73, 74, 78, 89, 92, 97, 111, 116, 121, 130, 137, 150, 154, 640, 642, 643, 654, 657] [7, 9, 13, 16, 18, 52, 58, 74, 75, 79, 90, 93, 98, 112, 117, 122, 131, 138, 151, 155, 641, 643, 644, 655, 658] [8, 10, 14, 17, 19, 40, 53, 59, 75, 76, 91, 94, 99, 113, 118, 123, 132, 139, 152, 156, 642, 644, 645, 656, 659] [9, 11, 15, 18, 20, 41, 54, 60, 76, 77, 92, 95, 100, 114, 119, 124, 133, 140, 153, 157, 643, 645, 646, 657, 660] [10, 12, 16, 19, 21, 42, 55, 61, 77, 78, 80, 93, 96, 101, 115, 125, 134, 141, 154, 158, 644, 646, 647, 658, 661] [11, 13, 17, 20, 22, 43, 56, 62, 78, 79, 81, 94, 97, 102, 116, 126, 135, 142, 155, 159, 645, 647, 648, 659, 662] [12, 14, 18, 21, 23, 40, 44, 57, 63, 79, 82, 95, 98, 103, 117, 120, 127, 136, 143, 156, 646, 648, 649, 660, 663] [13, 15, 19, 22, 24, 40, 41, 45, 58, 64, 83, 96, 99, 104, 118, 121, 128, 137, 144, 157, 647, 649, 650, 661, 664] [14, 16, 20, 23, 25, 41, 42, 46, 59, 65, 84, 97, 100, 105, 119, 122, 129, 138, 145, 158, 648, 650, 651, 662, 665] [15, 17, 21, 24, 26, 42, 43, 47, 60, 66, 80, 85, 98, 101, 106, 123, 130, 139, 146, 159, 649, 651, 652, 663, 666] [16, 18, 22, 25, 27, 43, 44, 48, 61, 67, 81, 86, 99, 102, 107, 120, 124, 131, 140, 147, 650, 652, 653, 664, 667] [17, 19, 23, 26, 28, 44, 45, 49, 62, 68, 82, 87, 100, 103, 108, 121, 125, 132, 141, 148, 651, 653, 654, 665, 668] [18, 20, 24, 27, 29, 45, 46, 50, 63, 69, 83, 88, 101, 104, 109, 122, 126, 133, 142, 149, 652, 654, 655, 666, 669] [19, 21, 25, 28, 30, 46, 47, 51, 64, 70, 84, 89, 102, 105, 110, 123, 127, 134, 143, 150, 653, 655, 656, 667, 670] [20, 22, 26, 29, 31, 47, 48, 52, 65, 71, 85, 90, 103, 106, 111, 124, 128, 135, 144, 151, 654, 656, 657, 668, 671] [21, 23, 27, 30, 32, 48, 49, 53, 66, 72, 86, 91, 104, 107, 112, 125, 129, 136, 145, 152, 655, 657, 658, 669, 672] [22, 24, 28, 31, 33, 49, 50, 54, 67, 73, 87, 92, 105, 108, 113, 126, 130, 137, 146, 153, 656, 658, 659, 670, 673] [23, 25, 29, 32, 34, 50, 51, 55, 68, 74, 88, 93, 106, 109, 114, 127, 131, 138, 147, 154, 657, 659, 660, 671, 674] [24, 26, 30, 33, 35, 51, 52, 56, 69, 75, 89, 94, 107, 110, 115, 128, 132, 139, 148, 155, 658, 660, 661, 672, 675] [25, 27, 31, 34, 36, 52, 53, 57, 70, 76, 90, 95, 108, 111, 116, 129, 133, 140, 149, 156, 659, 661, 662, 673, 676] [26, 28, 32, 35, 37, 53, 54, 58, 71, 77, 91, 96, 109, 112, 117, 130, 134, 141, 150, 157, 660, 662, 663, 674, 677] [27, 29, 33, 36, 38, 54, 55, 59, 72, 78, 92, 97, 110, 113, 118, 131, 135, 142, 151, 158, 661, 663, 664, 675, 678] [28, 30, 34, 37, 39, 55, 56, 60, 73, 79, 93, 98, 111, 114, 119, 132, 136, 143, 152, 159, 662, 664, 665, 676, 679] [160, 189, 191, 195, 198, 200, 216, 217, 221, 234, 240, 254, 259, 272, 275, 280, 293, 297, 304, 313, 640, 658, 664, 665, 673] [161, 190, 192, 196, 199, 201, 217, 218, 222, 235, 241, 255, 260, 273, 276, 281, 294, 298, 305, 314, 641, 659, 665, 666, 674] [160, 162, 191, 193, 197, 202, 218, 219, 223, 236, 242, 256, 261, 274, 277, 282, 295, 299, 306, 315, 642, 660, 666, 667, 675] [161, 163, 192, 194, 198, 203, 219, 220, 224, 237, 243, 257, 262, 275, 278, 283, 296, 300, 307, 316, 643, 661, 667, 668, 676] [162, 164, 193, 195, 199, 204, 220, 221, 225, 238, 244, 258, 263, 276, 279, 284, 297, 301, 308, 317, 644, 662, 668, 669, 677] [160, 163, 165, 194, 196, 205, 221, 222, 226, 239, 240, 245, 259, 264, 277, 285, 298, 302, 309, 318, 645, 663, 669, 670, 678] [161, 164, 166, 195, 197, 200, 206, 222, 223, 227, 241, 246, 260, 265, 278, 286, 299, 303, 310, 319, 646, 664, 670, 671, 679] [162, 165, 167, 196, 198, 201, 207, 223, 224, 228, 242, 247, 261, 266, 279, 280, 287, 300, 304, 311, 640, 647, 665, 671, 672] [163, 166, 168, 197, 199, 202, 208, 224, 225, 229, 240, 243, 248, 262, 267, 281, 288, 301, 305, 312, 641, 648, 666, 672, 673] [160, 164, 167, 169, 198, 203, 209, 225, 226, 230, 241, 244, 249, 263, 268, 282, 289, 302, 306, 313, 642, 649, 667, 673, 674] [161, 165, 168, 170, 199, 204, 210, 226, 227, 231, 242, 245, 250, 264, 269, 283, 290, 303, 307, 314, 643, 650, 668, 674, 675] [160, 162, 166, 169, 171, 205, 211, 227, 228, 232, 243, 246, 251, 265, 270, 284, 291, 304, 308, 315, 644, 651, 669, 675, 676] [161, 163, 167, 170, 172, 206, 212, 228, 229, 233, 244, 247, 252, 266, 271, 285, 292, 305, 309, 316, 645, 652, 670, 676, 677] [162, 164, 168, 171, 173, 207, 213, 229, 230, 234, 245, 248, 253, 267, 272, 286, 293, 306, 310, 317, 646, 653, 671, 677, 678] [163, 165, 169, 172, 174, 208, 214, 230, 231, 235, 246, 249, 254, 268, 273, 287, 294, 307, 311, 318, 647, 654, 672, 678, 679] [164, 166, 170, 173, 175, 209, 215, 231, 232, 236, 247, 250, 255, 269, 274, 288, 295, 308, 312, 319, 640, 648, 655, 673, 679] [165, 167, 171, 174, 176, 210, 216, 232, 233, 237, 248, 251, 256, 270, 275, 280, 289, 296, 309, 313, 640, 641, 649, 656, 674] [166, 168, 172, 175, 177, 211, 217, 233, 234, 238, 249, 252, 257, 271, 276, 281, 290, 297, 310, 314, 641, 642, 650, 657, 675] [167, 169, 173, 176, 178, 212, 218, 234, 235, 239, 250, 253, 258, 272, 277, 282, 291, 298, 311, 315, 642, 643, 651, 658, 676] [168, 170, 174, 177, 179, 200, 213, 219, 235, 236, 251, 254, 259, 273, 278, 283, 292, 299, 312, 316, 643, 644, 652, 659, 677] [169, 171, 175, 178, 180, 201, 214, 220, 236, 237, 252, 255, 260, 274, 279, 284, 293, 300, 313, 317, 644, 645, 653, 660, 678] [170, 172, 176, 179, 181, 202, 215, 221, 237, 238, 240, 253, 256, 261, 275, 285, 294, 301, 314, 318, 645, 646, 654, 661, 679] [171, 173, 177, 180, 182, 203, 216, 222, 238, 239, 241, 254, 257, 262, 276, 286, 295, 302, 315, 319, 640, 646, 647, 655, 662] [172, 174, 178, 181, 183, 200, 204, 217, 223, 239, 242, 255, 258, 263, 277, 280, 287, 296, 303, 316, 641, 647, 648, 656, 663] [173, 175, 179, 182, 184, 200, 201, 205, 218, 224, 243, 256, 259, 264, 278, 281, 288, 297, 304, 317, 642, 648, 649, 657, 664] [174, 176, 180, 183, 185, 201, 202, 206, 219, 225, 244, 257, 260, 265, 279, 282, 289, 298, 305, 318, 643, 649, 650, 658, 665] [175, 177, 181, 184, 186, 202, 203, 207, 220, 226, 240, 245, 258, 261, 266, 283, 290, 299, 306, 319, 644, 650, 651, 659, 666] [176, 178, 182, 185, 187, 203, 204, 208, 221, 227, 241, 246, 259, 262, 267, 280, 284, 291, 300, 307, 645, 651, 652, 660, 667] [177, 179, 183, 186, 188, 204, 205, 209, 222, 228, 242, 247, 260, 263, 268, 281, 285, 292, 301, 308, 646, 652, 653, 661, 668] [178, 180, 184, 187, 189, 205, 206, 210, 223, 229, 243, 248, 261, 264, 269, 282, 286, 293, 302, 309, 647, 653, 654, 662, 669] [179, 181, 185, 188, 190, 206, 207, 211, 224, 230, 244, 249, 262, 265, 270, 283, 287, 294, 303, 310, 648, 654, 655, 663, 670] [180, 182, 186, 189, 191, 207, 208, 212, 225, 231, 245, 250, 263, 266, 271, 284, 288, 295, 304, 311, 649, 655, 656, 664, 671] [181, 183, 187, 190, 192, 208, 209, 213, 226, 232, 246, 251, 264, 267, 272, 285, 289, 296, 305, 312, 650, 656, 657, 665, 672] [182, 184, 188, 191, 193, 209, 210, 214, 227, 233, 247, 252, 265, 268, 273, 286, 290, 297, 306, 313, 651, 657, 658, 666, 673] [183, 185, 189, 192, 194, 210, 211, 215, 228, 234, 248, 253, 266, 269, 274, 287, 291, 298, 307, 314, 652, 658, 659, 667, 674] [184, 186, 190, 193, 195, 211, 212, 216, 229, 235, 249, 254, 267, 270, 275, 288, 292, 299, 308, 315, 653, 659, 660, 668, 675] [185, 187, 191, 194, 196, 212, 213, 217, 230, 236, 250, 255, 268, 271, 276, 289, 293, 300, 309, 316, 654, 660, 661, 669, 676] [186, 188, 192, 195, 197, 213, 214, 218, 231, 237, 251, 256, 269, 272, 277, 290, 294, 301, 310, 317, 655, 661, 662, 670, 677] [187, 189, 193, 196, 198, 214, 215, 219, 232, 238, 252, 257, 270, 273, 278, 291, 295, 302, 311, 318, 656, 662, 663, 671, 678] [188, 190, 194, 197, 199, 215, 216, 220, 233, 239, 253, 258, 271, 274, 279, 292, 296, 303, 312, 319, 657, 663, 664, 672, 679] [320, 349, 351, 355, 358, 360, 376, 377, 381, 394, 400, 414, 419, 432, 435, 440, 453, 457, 464, 473, 640, 653, 659, 661, 668] [321, 350, 352, 356, 359, 361, 377, 378, 382, 395, 401, 415, 420, 433, 436, 441, 454, 458, 465, 474, 641, 654, 660, 662, 669] [320, 322, 351, 353, 357, 362, 378, 379, 383, 396, 402, 416, 421, 434, 437, 442, 455, 459, 466, 475, 642, 655, 661, 663, 670] [321, 323, 352, 354, 358, 363, 379, 380, 384, 397, 403, 417, 422, 435, 438, 443, 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Code ID 680-360-10 · download JSON · raw on GitHub