{ "schema_version": "0.1", "name": "[[672,336,12]] GALA rate-1/2 code", "code_type": "CSS", "n": 672, "k": 336, "checks": { "X": [ [ 61, 94, 119, 243, 260, 300, 363, 458, 472, 510, 614, 638 ], [ 62, 95, 120, 244, 261, 301, 350, 459, 473, 511, 615, 639 ], [ 63, 96, 121, 245, 262, 302, 351, 460, 474, 512, 602, 640 ], [ 64, 97, 122, 246, 263, 303, 352, 461, 475, 513, 603, 641 ], [ 65, 84, 123, 247, 264, 304, 353, 448, 462, 514, 604, 642 ], [ 66, 85, 124, 248, 265, 305, 354, 449, 463, 515, 605, 643 ], [ 67, 86, 125, 249, 252, 306, 355, 450, 464, 516, 606, 630 ], [ 68, 87, 112, 250, 253, 307, 356, 451, 465, 517, 607, 631 ], [ 69, 88, 113, 251, 254, 294, 357, 452, 466, 504, 608, 632 ], [ 56, 89, 114, 238, 255, 295, 358, 453, 467, 505, 609, 633 ], [ 57, 90, 115, 239, 256, 296, 359, 454, 468, 506, 610, 634 ], [ 58, 91, 116, 240, 257, 297, 360, 455, 469, 507, 611, 635 ], [ 59, 92, 117, 241, 258, 298, 361, 456, 470, 508, 612, 636 ], [ 60, 93, 118, 242, 259, 299, 362, 457, 471, 509, 613, 637 ], [ 75, 91, 108, 215, 274, 314, 377, 430, 486, 524, 628, 652 ], [ 76, 92, 109, 216, 275, 315, 364, 431, 487, 525, 629, 653 ], [ 77, 93, 110, 217, 276, 316, 365, 432, 488, 526, 616, 654 ], [ 78, 94, 111, 218, 277, 317, 366, 433, 489, 527, 617, 655 ], [ 79, 95, 98, 219, 278, 318, 367, 420, 476, 528, 618, 656 ], [ 80, 96, 99, 220, 279, 319, 368, 421, 477, 529, 619, 657 ], [ 81, 97, 100, 221, 266, 320, 369, 422, 478, 530, 620, 644 ], [ 82, 84, 101, 222, 267, 321, 370, 423, 479, 531, 621, 645 ], [ 83, 85, 102, 223, 268, 308, 371, 424, 480, 518, 622, 646 ], [ 70, 86, 103, 210, 269, 309, 372, 425, 481, 519, 623, 647 ], [ 71, 87, 104, 211, 270, 310, 373, 426, 482, 520, 624, 648 ], [ 72, 88, 105, 212, 271, 311, 374, 427, 483, 521, 625, 649 ], [ 73, 89, 106, 213, 272, 312, 375, 428, 484, 522, 626, 650 ], [ 74, 90, 107, 214, 273, 313, 376, 429, 485, 523, 627, 651 ], [ 47, 105, 122, 229, 288, 328, 349, 444, 500, 538, 600, 666 ], [ 48, 106, 123, 230, 289, 329, 336, 445, 501, 539, 601, 667 ], [ 49, 107, 124, 231, 290, 330, 337, 446, 502, 540, 588, 668 ], [ 50, 108, 125, 232, 291, 331, 338, 447, 503, 541, 589, 669 ], [ 51, 109, 112, 233, 292, 332, 339, 434, 490, 542, 590, 670 ], [ 52, 110, 113, 234, 293, 333, 340, 435, 491, 543, 591, 671 ], [ 53, 111, 114, 235, 280, 334, 341, 436, 492, 544, 592, 658 ], [ 54, 98, 115, 236, 281, 335, 342, 437, 493, 545, 593, 659 ], [ 55, 99, 116, 237, 282, 322, 343, 438, 494, 532, 594, 660 ], [ 42, 100, 117, 224, 283, 323, 344, 439, 495, 533, 595, 661 ], [ 43, 101, 118, 225, 284, 324, 345, 440, 496, 534, 596, 662 ], [ 44, 102, 119, 226, 285, 325, 346, 441, 497, 535, 597, 663 ], [ 45, 103, 120, 227, 286, 326, 347, 442, 498, 536, 598, 664 ], [ 46, 104, 121, 228, 287, 327, 348, 443, 499, 537, 599, 665 ], [ 19, 136, 161, 201, 258, 302, 405, 430, 500, 552, 596, 656 ], [ 20, 137, 162, 202, 259, 303, 392, 431, 501, 553, 597, 657 ], [ 21, 138, 163, 203, 260, 304, 393, 432, 502, 554, 598, 644 ], [ 22, 139, 164, 204, 261, 305, 394, 433, 503, 555, 599, 645 ], [ 23, 126, 165, 205, 262, 306, 395, 420, 490, 556, 600, 646 ], [ 24, 127, 166, 206, 263, 307, 396, 421, 491, 557, 601, 647 ], [ 25, 128, 167, 207, 264, 294, 397, 422, 492, 558, 588, 648 ], [ 26, 129, 154, 208, 265, 295, 398, 423, 493, 559, 589, 649 ], [ 27, 130, 155, 209, 252, 296, 399, 424, 494, 546, 590, 650 ], [ 14, 131, 156, 196, 253, 297, 400, 425, 495, 547, 591, 651 ], [ 15, 132, 157, 197, 254, 298, 401, 426, 496, 548, 592, 652 ], [ 16, 133, 158, 198, 255, 299, 402, 427, 497, 549, 593, 653 ], [ 17, 134, 159, 199, 256, 300, 403, 428, 498, 550, 594, 654 ], [ 18, 135, 160, 200, 257, 301, 404, 429, 499, 551, 595, 655 ], [ 33, 133, 150, 173, 272, 316, 419, 444, 472, 566, 610, 670 ], [ 34, 134, 151, 174, 273, 317, 406, 445, 473, 567, 611, 671 ], [ 35, 135, 152, 175, 274, 318, 407, 446, 474, 568, 612, 658 ], [ 36, 136, 153, 176, 275, 319, 408, 447, 475, 569, 613, 659 ], [ 37, 137, 140, 177, 276, 320, 409, 434, 462, 570, 614, 660 ], [ 38, 138, 141, 178, 277, 321, 410, 435, 463, 571, 615, 661 ], [ 39, 139, 142, 179, 278, 308, 411, 436, 464, 572, 602, 662 ], [ 40, 126, 143, 180, 279, 309, 412, 437, 465, 573, 603, 663 ], [ 41, 127, 144, 181, 266, 310, 413, 438, 466, 560, 604, 664 ], [ 28, 128, 145, 168, 267, 311, 414, 439, 467, 561, 605, 665 ], [ 29, 129, 146, 169, 268, 312, 415, 440, 468, 562, 606, 666 ], [ 30, 130, 147, 170, 269, 313, 416, 441, 469, 563, 607, 667 ], [ 31, 131, 148, 171, 270, 314, 417, 442, 470, 564, 608, 668 ], [ 32, 132, 149, 172, 271, 315, 418, 443, 471, 565, 609, 669 ], [ 5, 147, 164, 187, 286, 330, 391, 458, 486, 580, 624, 642 ], [ 6, 148, 165, 188, 287, 331, 378, 459, 487, 581, 625, 643 ], [ 7, 149, 166, 189, 288, 332, 379, 460, 488, 582, 626, 630 ], [ 8, 150, 167, 190, 289, 333, 380, 461, 489, 583, 627, 631 ], [ 9, 151, 154, 191, 290, 334, 381, 448, 476, 584, 628, 632 ], [ 10, 152, 155, 192, 291, 335, 382, 449, 477, 585, 629, 633 ], [ 11, 153, 156, 193, 292, 322, 383, 450, 478, 586, 616, 634 ], [ 12, 140, 157, 194, 293, 323, 384, 451, 479, 587, 617, 635 ], [ 13, 141, 158, 195, 280, 324, 385, 452, 480, 574, 618, 636 ], [ 0, 142, 159, 182, 281, 325, 386, 453, 481, 575, 619, 637 ], [ 1, 143, 160, 183, 282, 326, 387, 454, 482, 576, 620, 638 ], [ 2, 144, 161, 184, 283, 327, 388, 455, 483, 577, 621, 639 ], [ 3, 145, 162, 185, 284, 328, 389, 456, 484, 578, 622, 640 ], [ 4, 146, 163, 186, 285, 329, 390, 457, 485, 579, 623, 641 ], [ 8, 48, 145, 178, 203, 327, 362, 386, 447, 542, 556, 594 ], [ 9, 49, 146, 179, 204, 328, 363, 387, 434, 543, 557, 595 ], [ 10, 50, 147, 180, 205, 329, 350, 388, 435, 544, 558, 596 ], [ 11, 51, 148, 181, 206, 330, 351, 389, 436, 545, 559, 597 ], [ 12, 52, 149, 168, 207, 331, 352, 390, 437, 532, 546, 598 ], [ 13, 53, 150, 169, 208, 332, 353, 391, 438, 533, 547, 599 ], [ 0, 54, 151, 170, 209, 333, 354, 378, 439, 534, 548, 600 ], [ 1, 55, 152, 171, 196, 334, 355, 379, 440, 535, 549, 601 ], [ 2, 42, 153, 172, 197, 335, 356, 380, 441, 536, 550, 588 ], [ 3, 43, 140, 173, 198, 322, 357, 381, 442, 537, 551, 589 ], [ 4, 44, 141, 174, 199, 323, 358, 382, 443, 538, 552, 590 ], [ 5, 45, 142, 175, 200, 324, 359, 383, 444, 539, 553, 591 ], [ 6, 46, 143, 176, 201, 325, 360, 384, 445, 540, 554, 592 ], [ 7, 47, 144, 177, 202, 326, 361, 385, 446, 541, 555, 593 ], [ 22, 62, 159, 175, 192, 299, 376, 400, 461, 514, 570, 608 ], [ 23, 63, 160, 176, 193, 300, 377, 401, 448, 515, 571, 609 ], [ 24, 64, 161, 177, 194, 301, 364, 402, 449, 516, 572, 610 ], [ 25, 65, 162, 178, 195, 302, 365, 403, 450, 517, 573, 611 ], [ 26, 66, 163, 179, 182, 303, 366, 404, 451, 504, 560, 612 ], [ 27, 67, 164, 180, 183, 304, 367, 405, 452, 505, 561, 613 ], [ 14, 68, 165, 181, 184, 305, 368, 392, 453, 506, 562, 614 ], [ 15, 69, 166, 168, 185, 306, 369, 393, 454, 507, 563, 615 ], [ 16, 56, 167, 169, 186, 307, 370, 394, 455, 508, 564, 602 ], [ 17, 57, 154, 170, 187, 294, 371, 395, 456, 509, 565, 603 ], [ 18, 58, 155, 171, 188, 295, 372, 396, 457, 510, 566, 604 ], [ 19, 59, 156, 172, 189, 296, 373, 397, 458, 511, 567, 605 ], [ 20, 60, 157, 173, 190, 297, 374, 398, 459, 512, 568, 606 ], [ 21, 61, 158, 174, 191, 298, 375, 399, 460, 513, 569, 607 ], [ 36, 76, 131, 189, 206, 313, 348, 414, 433, 528, 584, 622 ], [ 37, 77, 132, 190, 207, 314, 349, 415, 420, 529, 585, 623 ], [ 38, 78, 133, 191, 208, 315, 336, 416, 421, 530, 586, 624 ], [ 39, 79, 134, 192, 209, 316, 337, 417, 422, 531, 587, 625 ], [ 40, 80, 135, 193, 196, 317, 338, 418, 423, 518, 574, 626 ], [ 41, 81, 136, 194, 197, 318, 339, 419, 424, 519, 575, 627 ], [ 28, 82, 137, 195, 198, 319, 340, 406, 425, 520, 576, 628 ], [ 29, 83, 138, 182, 199, 320, 341, 407, 426, 521, 577, 629 ], [ 30, 70, 139, 183, 200, 321, 342, 408, 427, 522, 578, 616 ], [ 31, 71, 126, 184, 201, 308, 343, 409, 428, 523, 579, 617 ], [ 32, 72, 127, 185, 202, 309, 344, 410, 429, 524, 580, 618 ], [ 33, 73, 128, 186, 203, 310, 345, 411, 430, 525, 581, 619 ], [ 34, 74, 129, 187, 204, 311, 346, 412, 431, 526, 582, 620 ], [ 35, 75, 130, 188, 205, 312, 347, 413, 432, 527, 583, 621 ], [ 6, 50, 103, 220, 245, 285, 344, 404, 489, 514, 584, 636 ], [ 7, 51, 104, 221, 246, 286, 345, 405, 476, 515, 585, 637 ], [ 8, 52, 105, 222, 247, 287, 346, 392, 477, 516, 586, 638 ], [ 9, 53, 106, 223, 248, 288, 347, 393, 478, 517, 587, 639 ], [ 10, 54, 107, 210, 249, 289, 348, 394, 479, 504, 574, 640 ], [ 11, 55, 108, 211, 250, 290, 349, 395, 480, 505, 575, 641 ], [ 12, 42, 109, 212, 251, 291, 336, 396, 481, 506, 576, 642 ], [ 13, 43, 110, 213, 238, 292, 337, 397, 482, 507, 577, 643 ], [ 0, 44, 111, 214, 239, 293, 338, 398, 483, 508, 578, 630 ], [ 1, 45, 98, 215, 240, 280, 339, 399, 484, 509, 579, 631 ], [ 2, 46, 99, 216, 241, 281, 340, 400, 485, 510, 580, 632 ], [ 3, 47, 100, 217, 242, 282, 341, 401, 486, 511, 581, 633 ], [ 4, 48, 101, 218, 243, 283, 342, 402, 487, 512, 582, 634 ], [ 5, 49, 102, 219, 244, 284, 343, 403, 488, 513, 583, 635 ], [ 20, 64, 117, 217, 234, 257, 358, 418, 503, 528, 556, 650 ], [ 21, 65, 118, 218, 235, 258, 359, 419, 490, 529, 557, 651 ], [ 22, 66, 119, 219, 236, 259, 360, 406, 491, 530, 558, 652 ], [ 23, 67, 120, 220, 237, 260, 361, 407, 492, 531, 559, 653 ], [ 24, 68, 121, 221, 224, 261, 362, 408, 493, 518, 546, 654 ], [ 25, 69, 122, 222, 225, 262, 363, 409, 494, 519, 547, 655 ], [ 26, 56, 123, 223, 226, 263, 350, 410, 495, 520, 548, 656 ], [ 27, 57, 124, 210, 227, 264, 351, 411, 496, 521, 549, 657 ], [ 14, 58, 125, 211, 228, 265, 352, 412, 497, 522, 550, 644 ], [ 15, 59, 112, 212, 229, 252, 353, 413, 498, 523, 551, 645 ], [ 16, 60, 113, 213, 230, 253, 354, 414, 499, 524, 552, 646 ], [ 17, 61, 114, 214, 231, 254, 355, 415, 500, 525, 553, 647 ], [ 18, 62, 115, 215, 232, 255, 356, 416, 501, 526, 554, 648 ], [ 19, 63, 116, 216, 233, 256, 357, 417, 502, 527, 555, 649 ], [ 34, 78, 89, 231, 248, 271, 372, 390, 475, 542, 570, 664 ], [ 35, 79, 90, 232, 249, 272, 373, 391, 462, 543, 571, 665 ], [ 36, 80, 91, 233, 250, 273, 374, 378, 463, 544, 572, 666 ], [ 37, 81, 92, 234, 251, 274, 375, 379, 464, 545, 573, 667 ], [ 38, 82, 93, 235, 238, 275, 376, 380, 465, 532, 560, 668 ], [ 39, 83, 94, 236, 239, 276, 377, 381, 466, 533, 561, 669 ], [ 40, 70, 95, 237, 240, 277, 364, 382, 467, 534, 562, 670 ], [ 41, 71, 96, 224, 241, 278, 365, 383, 468, 535, 563, 671 ], [ 28, 72, 97, 225, 242, 279, 366, 384, 469, 536, 564, 658 ], [ 29, 73, 84, 226, 243, 266, 367, 385, 470, 537, 565, 659 ], [ 30, 74, 85, 227, 244, 267, 368, 386, 471, 538, 566, 660 ], [ 31, 75, 86, 228, 245, 268, 369, 387, 472, 539, 567, 661 ], [ 32, 76, 87, 229, 246, 269, 370, 388, 473, 540, 568, 662 ], [ 33, 77, 88, 230, 247, 270, 371, 389, 474, 541, 569, 663 ] ], "Z": [ [ 29, 114, 132, 176, 270, 298, 415, 426, 470, 569, 592, 609 ], [ 30, 115, 133, 177, 271, 299, 416, 427, 471, 570, 593, 610 ], [ 31, 116, 134, 178, 272, 300, 417, 428, 472, 571, 594, 611 ], [ 32, 117, 135, 179, 273, 301, 418, 429, 473, 572, 595, 612 ], [ 33, 118, 136, 180, 274, 302, 419, 430, 474, 573, 596, 613 ], [ 34, 119, 137, 181, 275, 303, 406, 431, 475, 560, 597, 614 ], [ 35, 120, 138, 168, 276, 304, 407, 432, 462, 561, 598, 615 ], [ 36, 121, 139, 169, 277, 305, 408, 433, 463, 562, 599, 602 ], [ 37, 122, 126, 170, 278, 306, 409, 420, 464, 563, 600, 603 ], [ 38, 123, 127, 171, 279, 307, 410, 421, 465, 564, 601, 604 ], [ 39, 124, 128, 172, 266, 294, 411, 422, 466, 565, 588, 605 ], [ 40, 125, 129, 173, 267, 295, 412, 423, 467, 566, 589, 606 ], [ 41, 112, 130, 174, 268, 296, 413, 424, 468, 567, 590, 607 ], [ 28, 113, 131, 175, 269, 297, 414, 425, 469, 568, 591, 608 ], [ 1, 86, 146, 190, 284, 312, 387, 440, 484, 583, 606, 623 ], [ 2, 87, 147, 191, 285, 313, 388, 441, 485, 584, 607, 624 ], [ 3, 88, 148, 192, 286, 314, 389, 442, 486, 585, 608, 625 ], [ 4, 89, 149, 193, 287, 315, 390, 443, 487, 586, 609, 626 ], [ 5, 90, 150, 194, 288, 316, 391, 444, 488, 587, 610, 627 ], [ 6, 91, 151, 195, 289, 317, 378, 445, 489, 574, 611, 628 ], [ 7, 92, 152, 182, 290, 318, 379, 446, 476, 575, 612, 629 ], [ 8, 93, 153, 183, 291, 319, 380, 447, 477, 576, 613, 616 ], [ 9, 94, 140, 184, 292, 320, 381, 434, 478, 577, 614, 617 ], [ 10, 95, 141, 185, 293, 321, 382, 435, 479, 578, 615, 618 ], [ 11, 96, 142, 186, 280, 308, 383, 436, 480, 579, 602, 619 ], [ 12, 97, 143, 187, 281, 309, 384, 437, 481, 580, 603, 620 ], [ 13, 84, 144, 188, 282, 310, 385, 438, 482, 581, 604, 621 ], [ 0, 85, 145, 189, 283, 311, 386, 439, 483, 582, 605, 622 ], [ 15, 100, 160, 204, 256, 326, 401, 454, 498, 555, 595, 620 ], [ 16, 101, 161, 205, 257, 327, 402, 455, 499, 556, 596, 621 ], [ 17, 102, 162, 206, 258, 328, 403, 456, 500, 557, 597, 622 ], [ 18, 103, 163, 207, 259, 329, 404, 457, 501, 558, 598, 623 ], [ 19, 104, 164, 208, 260, 330, 405, 458, 502, 559, 599, 624 ], [ 20, 105, 165, 209, 261, 331, 392, 459, 503, 546, 600, 625 ], [ 21, 106, 166, 196, 262, 332, 393, 460, 490, 547, 601, 626 ], [ 22, 107, 167, 197, 263, 333, 394, 461, 491, 548, 588, 627 ], [ 23, 108, 154, 198, 264, 334, 395, 448, 492, 549, 589, 628 ], [ 24, 109, 155, 199, 265, 335, 396, 449, 493, 550, 590, 629 ], [ 25, 110, 156, 200, 252, 322, 397, 450, 494, 551, 591, 616 ], [ 26, 111, 157, 201, 253, 323, 398, 451, 495, 552, 592, 617 ], [ 27, 98, 158, 202, 254, 324, 399, 452, 496, 553, 593, 618 ], [ 14, 99, 159, 203, 255, 325, 400, 453, 497, 554, 594, 619 ], [ 71, 90, 156, 218, 256, 312, 373, 428, 468, 527, 634, 651 ], [ 72, 91, 157, 219, 257, 313, 374, 429, 469, 528, 635, 652 ], [ 73, 92, 158, 220, 258, 314, 375, 430, 470, 529, 636, 653 ], [ 74, 93, 159, 221, 259, 315, 376, 431, 471, 530, 637, 654 ], [ 75, 94, 160, 222, 260, 316, 377, 432, 472, 531, 638, 655 ], [ 76, 95, 161, 223, 261, 317, 364, 433, 473, 518, 639, 656 ], [ 77, 96, 162, 210, 262, 318, 365, 420, 474, 519, 640, 657 ], [ 78, 97, 163, 211, 263, 319, 366, 421, 475, 520, 641, 644 ], [ 79, 84, 164, 212, 264, 320, 367, 422, 462, 521, 642, 645 ], [ 80, 85, 165, 213, 265, 321, 368, 423, 463, 522, 643, 646 ], [ 81, 86, 166, 214, 252, 308, 369, 424, 464, 523, 630, 647 ], [ 82, 87, 167, 215, 253, 309, 370, 425, 465, 524, 631, 648 ], [ 83, 88, 154, 216, 254, 310, 371, 426, 466, 525, 632, 649 ], [ 70, 89, 155, 217, 255, 311, 372, 427, 467, 526, 633, 650 ], [ 43, 104, 128, 232, 270, 326, 345, 442, 482, 541, 648, 665 ], [ 44, 105, 129, 233, 271, 327, 346, 443, 483, 542, 649, 666 ], [ 45, 106, 130, 234, 272, 328, 347, 444, 484, 543, 650, 667 ], [ 46, 107, 131, 235, 273, 329, 348, 445, 485, 544, 651, 668 ], [ 47, 108, 132, 236, 274, 330, 349, 446, 486, 545, 652, 669 ], [ 48, 109, 133, 237, 275, 331, 336, 447, 487, 532, 653, 670 ], [ 49, 110, 134, 224, 276, 332, 337, 434, 488, 533, 654, 671 ], [ 50, 111, 135, 225, 277, 333, 338, 435, 489, 534, 655, 658 ], [ 51, 98, 136, 226, 278, 334, 339, 436, 476, 535, 656, 659 ], [ 52, 99, 137, 227, 279, 335, 340, 437, 477, 536, 657, 660 ], [ 53, 100, 138, 228, 266, 322, 341, 438, 478, 537, 644, 661 ], [ 54, 101, 139, 229, 267, 323, 342, 439, 479, 538, 645, 662 ], [ 55, 102, 126, 230, 268, 324, 343, 440, 480, 539, 646, 663 ], [ 42, 103, 127, 231, 269, 325, 344, 441, 481, 540, 647, 664 ], [ 57, 118, 142, 246, 284, 298, 359, 456, 496, 513, 637, 662 ], [ 58, 119, 143, 247, 285, 299, 360, 457, 497, 514, 638, 663 ], [ 59, 120, 144, 248, 286, 300, 361, 458, 498, 515, 639, 664 ], [ 60, 121, 145, 249, 287, 301, 362, 459, 499, 516, 640, 665 ], [ 61, 122, 146, 250, 288, 302, 363, 460, 500, 517, 641, 666 ], [ 62, 123, 147, 251, 289, 303, 350, 461, 501, 504, 642, 667 ], [ 63, 124, 148, 238, 290, 304, 351, 448, 502, 505, 643, 668 ], [ 64, 125, 149, 239, 291, 305, 352, 449, 503, 506, 630, 669 ], [ 65, 112, 150, 240, 292, 306, 353, 450, 490, 507, 631, 670 ], [ 66, 113, 151, 241, 293, 307, 354, 451, 491, 508, 632, 671 ], [ 67, 114, 152, 242, 280, 294, 355, 452, 492, 509, 633, 658 ], [ 68, 115, 153, 243, 281, 295, 356, 453, 493, 510, 634, 659 ], [ 69, 116, 140, 244, 282, 296, 357, 454, 494, 511, 635, 660 ], [ 56, 117, 141, 245, 283, 297, 358, 455, 495, 512, 636, 661 ], [ 18, 46, 113, 198, 216, 260, 340, 357, 499, 510, 554, 653 ], [ 19, 47, 114, 199, 217, 261, 341, 358, 500, 511, 555, 654 ], [ 20, 48, 115, 200, 218, 262, 342, 359, 501, 512, 556, 655 ], [ 21, 49, 116, 201, 219, 263, 343, 360, 502, 513, 557, 656 ], [ 22, 50, 117, 202, 220, 264, 344, 361, 503, 514, 558, 657 ], [ 23, 51, 118, 203, 221, 265, 345, 362, 490, 515, 559, 644 ], [ 24, 52, 119, 204, 222, 252, 346, 363, 491, 516, 546, 645 ], [ 25, 53, 120, 205, 223, 253, 347, 350, 492, 517, 547, 646 ], [ 26, 54, 121, 206, 210, 254, 348, 351, 493, 504, 548, 647 ], [ 27, 55, 122, 207, 211, 255, 349, 352, 494, 505, 549, 648 ], [ 14, 42, 123, 208, 212, 256, 336, 353, 495, 506, 550, 649 ], [ 15, 43, 124, 209, 213, 257, 337, 354, 496, 507, 551, 650 ], [ 16, 44, 125, 196, 214, 258, 338, 355, 497, 508, 552, 651 ], [ 17, 45, 112, 197, 215, 259, 339, 356, 498, 509, 553, 652 ], [ 32, 60, 85, 170, 230, 274, 354, 371, 471, 524, 568, 667 ], [ 33, 61, 86, 171, 231, 275, 355, 372, 472, 525, 569, 668 ], [ 34, 62, 87, 172, 232, 276, 356, 373, 473, 526, 570, 669 ], [ 35, 63, 88, 173, 233, 277, 357, 374, 474, 527, 571, 670 ], [ 36, 64, 89, 174, 234, 278, 358, 375, 475, 528, 572, 671 ], [ 37, 65, 90, 175, 235, 279, 359, 376, 462, 529, 573, 658 ], [ 38, 66, 91, 176, 236, 266, 360, 377, 463, 530, 560, 659 ], [ 39, 67, 92, 177, 237, 267, 361, 364, 464, 531, 561, 660 ], [ 40, 68, 93, 178, 224, 268, 362, 365, 465, 518, 562, 661 ], [ 41, 69, 94, 179, 225, 269, 363, 366, 466, 519, 563, 662 ], [ 28, 56, 95, 180, 226, 270, 350, 367, 467, 520, 564, 663 ], [ 29, 57, 96, 181, 227, 271, 351, 368, 468, 521, 565, 664 ], [ 30, 58, 97, 168, 228, 272, 352, 369, 469, 522, 566, 665 ], [ 31, 59, 84, 169, 229, 273, 353, 370, 470, 523, 567, 666 ], [ 4, 74, 99, 184, 244, 288, 343, 368, 485, 538, 582, 639 ], [ 5, 75, 100, 185, 245, 289, 344, 369, 486, 539, 583, 640 ], [ 6, 76, 101, 186, 246, 290, 345, 370, 487, 540, 584, 641 ], [ 7, 77, 102, 187, 247, 291, 346, 371, 488, 541, 585, 642 ], [ 8, 78, 103, 188, 248, 292, 347, 372, 489, 542, 586, 643 ], [ 9, 79, 104, 189, 249, 293, 348, 373, 476, 543, 587, 630 ], [ 10, 80, 105, 190, 250, 280, 349, 374, 477, 544, 574, 631 ], [ 11, 81, 106, 191, 251, 281, 336, 375, 478, 545, 575, 632 ], [ 12, 82, 107, 192, 238, 282, 337, 376, 479, 532, 576, 633 ], [ 13, 83, 108, 193, 239, 283, 338, 377, 480, 533, 577, 634 ], [ 0, 70, 109, 194, 240, 284, 339, 364, 481, 534, 578, 635 ], [ 1, 71, 110, 195, 241, 285, 340, 365, 482, 535, 579, 636 ], [ 2, 72, 111, 182, 242, 286, 341, 366, 483, 536, 580, 637 ], [ 3, 73, 98, 183, 243, 287, 342, 367, 484, 537, 581, 638 ], [ 4, 60, 155, 174, 240, 302, 382, 399, 457, 512, 552, 611 ], [ 5, 61, 156, 175, 241, 303, 383, 400, 458, 513, 553, 612 ], [ 6, 62, 157, 176, 242, 304, 384, 401, 459, 514, 554, 613 ], [ 7, 63, 158, 177, 243, 305, 385, 402, 460, 515, 555, 614 ], [ 8, 64, 159, 178, 244, 306, 386, 403, 461, 516, 556, 615 ], [ 9, 65, 160, 179, 245, 307, 387, 404, 448, 517, 557, 602 ], [ 10, 66, 161, 180, 246, 294, 388, 405, 449, 504, 558, 603 ], [ 11, 67, 162, 181, 247, 295, 389, 392, 450, 505, 559, 604 ], [ 12, 68, 163, 168, 248, 296, 390, 393, 451, 506, 546, 605 ], [ 13, 69, 164, 169, 249, 297, 391, 394, 452, 507, 547, 606 ], [ 0, 56, 165, 170, 250, 298, 378, 395, 453, 508, 548, 607 ], [ 1, 57, 166, 171, 251, 299, 379, 396, 454, 509, 549, 608 ], [ 2, 58, 167, 172, 238, 300, 380, 397, 455, 510, 550, 609 ], [ 3, 59, 154, 173, 239, 301, 381, 398, 456, 511, 551, 610 ], [ 18, 74, 127, 188, 212, 316, 396, 413, 429, 526, 566, 625 ], [ 19, 75, 128, 189, 213, 317, 397, 414, 430, 527, 567, 626 ], [ 20, 76, 129, 190, 214, 318, 398, 415, 431, 528, 568, 627 ], [ 21, 77, 130, 191, 215, 319, 399, 416, 432, 529, 569, 628 ], [ 22, 78, 131, 192, 216, 320, 400, 417, 433, 530, 570, 629 ], [ 23, 79, 132, 193, 217, 321, 401, 418, 420, 531, 571, 616 ], [ 24, 80, 133, 194, 218, 308, 402, 419, 421, 518, 572, 617 ], [ 25, 81, 134, 195, 219, 309, 403, 406, 422, 519, 573, 618 ], [ 26, 82, 135, 182, 220, 310, 404, 407, 423, 520, 560, 619 ], [ 27, 83, 136, 183, 221, 311, 405, 408, 424, 521, 561, 620 ], [ 14, 70, 137, 184, 222, 312, 392, 409, 425, 522, 562, 621 ], [ 15, 71, 138, 185, 223, 313, 393, 410, 426, 523, 563, 622 ], [ 16, 72, 139, 186, 210, 314, 394, 411, 427, 524, 564, 623 ], [ 17, 73, 126, 187, 211, 315, 395, 412, 428, 525, 565, 624 ], [ 32, 46, 141, 202, 226, 330, 385, 410, 443, 540, 580, 597 ], [ 33, 47, 142, 203, 227, 331, 386, 411, 444, 541, 581, 598 ], [ 34, 48, 143, 204, 228, 332, 387, 412, 445, 542, 582, 599 ], [ 35, 49, 144, 205, 229, 333, 388, 413, 446, 543, 583, 600 ], [ 36, 50, 145, 206, 230, 334, 389, 414, 447, 544, 584, 601 ], [ 37, 51, 146, 207, 231, 335, 390, 415, 434, 545, 585, 588 ], [ 38, 52, 147, 208, 232, 322, 391, 416, 435, 532, 586, 589 ], [ 39, 53, 148, 209, 233, 323, 378, 417, 436, 533, 587, 590 ], [ 40, 54, 149, 196, 234, 324, 379, 418, 437, 534, 574, 591 ], [ 41, 55, 150, 197, 235, 325, 380, 419, 438, 535, 575, 592 ], [ 28, 42, 151, 198, 236, 326, 381, 406, 439, 536, 576, 593 ], [ 29, 43, 152, 199, 237, 327, 382, 407, 440, 537, 577, 594 ], [ 30, 44, 153, 200, 224, 328, 383, 408, 441, 538, 578, 595 ], [ 31, 45, 140, 201, 225, 329, 384, 409, 442, 539, 579, 596 ] ] }, "distance": { "d": 12, "X": { "value": 12, "confidence": "upper_bound", "witness": [ 159, 161, 165, 433, 459, 461, 463, 499, 504, 530, 548, 554 ] }, "Z": { "value": 12, "confidence": "upper_bound", "witness": [ 113, 136, 234, 251, 291, 382, 419, 447, 490, 552, 556, 670 ] } }, "provenance": { "authors": [ "Yang, Willers", "Duckering, Casey", "Dua, Arpit" ], "construction": "GALA code (group-action lift with active orthogonality), L=8, J=2, abelian group C_2 x C_3 x C_14 (trivial non-abelian factor, 'trivial top'). Block-circulant parents Hhat_X=[F|G], Hhat_Z=[G^T|F^T] over F_2[Z_4 x C_2 x C_3 x C_14] with F=(x^(1,1,5), x^(0,2,7)+x^(0,0,10), x^(1,2,5), x^(1,0,6)+x^(0,0,8)) and G=(x^(0,1,13), x^(1,0,10)+x^(0,2,10), x^(0,0,6), x^(1,0,8)+x^(0,1,12)); the first J=2 of L/2=4 block rows are kept as H_X, H_Z. Polynomial (binomial) lift entries give weight 12 at L=8; girth 6, rate exactly 1/2, d=w structural ceiling.", "origin": "baseline", "date": "2026-08-07", "references": [ "arXiv:2608.07431" ], "notes": "Distance d=12 certified exactly in arXiv:2608.07431 (Table S3; exhaustive exclusion of all lower-weight logicals plus an explicit weight-12 witness), at the structural ceiling d=w=12. Rebuilt here from the published generators \u2014 no parity-check matrices are distributed with the preprint; the rebuild reproduces n=672, k=336 at rate exactly 1/2 (rank H_X = rank H_Z = 168, full rank), weight 12, girth 6 (zero 4-cycles) and the paper's \"trivial top\" (H_X H_Z^T = 0 identically, the lift being abelian). Distinct from the [[672,340,8]] row of the same table despite the shared n. Witnesses recorded here are decoder-found weight-12 logicals (upper bound)." }, "family": "generalized-bicycle" }