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61, 110, 162, 211, 295, 302, 335, 366, 375, 483, 492, 535, 596, 608 ], [ 17, 28, 99, 127, 137, 141, 236, 308, 378, 391, 409, 462, 501, 534, 541, 542 ], [ 38, 59, 132, 167, 195, 258, 278, 309, 379, 392, 405, 463, 502, 530, 542, 543 ], [ 28, 79, 86, 113, 115, 209, 249, 305, 375, 393, 406, 464, 503, 531, 543, 544 ], [ 59, 74, 105, 155, 177, 185, 236, 306, 376, 394, 407, 460, 504, 532, 540, 544 ], [ 6, 48, 66, 115, 167, 216, 300, 307, 377, 390, 408, 461, 500, 533, 540, 541 ] ] }, "distance": { "d": 70, "X": { "value": 84, "confidence": "upper_bound", "witness": [ 4, 6, 8, 11, 12, 14, 18, 19, 27, 28, 33, 36, 42, 51, 59, 62, 64, 66, 67, 73, 78, 82, 85, 87, 89, 91, 94, 95, 98, 104, 105, 109, 118, 121, 123, 127, 131, 134, 138, 144, 145, 154, 159, 161, 163, 166, 167, 169, 173, 174, 182, 183, 188, 191, 197, 206, 214, 217, 219, 221, 222, 228, 233, 237, 240, 242, 244, 246, 249, 250, 253, 259, 260, 264, 273, 276, 278, 282, 286, 289, 293, 299, 300, 309 ] }, "Z": { "value": 70, "confidence": "upper_bound", "witness": [ 310, 313, 316, 317, 319, 327, 330, 331, 333, 336, 340, 350, 356, 360, 362, 367, 376, 378, 381, 383, 384, 388, 407, 409, 415, 417, 419, 424, 429, 431, 434, 440, 442, 443, 463, 465, 468, 471, 472, 474, 482, 485, 486, 488, 491, 495, 505, 511, 515, 517, 522, 531, 533, 536, 538, 539, 543, 562, 564, 570, 572, 574, 579, 584, 586, 589, 595, 597, 598, 618 ] } }, "provenance": { "authors": [ "@Ronaldoengenhariadacomputacao", "Ronaldo Rodrigues" ], "construction": "Two-block group algebra (2BGA) code on the metacyclic group C_62 |x_33 C_5 (order 310, r=33, ord(33,62)=5): H_X=[L(a)|R(b)], H_Z=[R(b)^T|L(a)^T] via left/right regular representations of a non-abelian group (they always commute for any group, no abelian requirement -- generalizes generalized-bicycle/circulant constructions). Weight-8 random group-algebra elements a,b found via RIS triage sweep (150 trials) over 486 metacyclic groups with n<=700 (within verify/qldpc_verify.py::admissible()'s unrestricted tier -- an earlier n=930 candidate with the same method was rejected by this repo's own schema cap and is not submitted), then confirmed with 20000-trial parallel RIS deepening (8 workers), stable from 6000 to 20000 trials.", "origin": "submission", "date": "2026-10-03", "model": "Claude Sonnet 5", "notes": "Distance via this repository's own RIS engine (verify/heuristic_distance.py::ris_min_logical, copied locally and cross-validated against this board's own #1 entry [[682,172,78]], where it found a lighter Z witness than published). Beats the best previously published 2bga-coset entry (n=684,k=10,d=90,kd2/n=118.42) by ~3x. CORRECTION: initial submission claimed d_X=104 from this repo-s own RIS engine at 20000 trials; the CI verify gate (gf2_fast accelerator, 8,000,000 trials) found a lighter X-logical of weight 96, refuting that claim. Updated to d_X=96 using the CI-provided witness directly (verified: it lies in ker(H_Z), not in rowspace(H_X)). d_Z=107 unchanged (not refuted). This is expected RIS behavior, not a construction error: a larger trial budget (ours lacked the gf2_fast accelerator) finds tighter upper bounds, consistent with how every upper_bound entry on this board works. SECOND CORRECTION (2026-10-03, @vprusso at review): the single-block annihilator attack of #2364 and #2365 (information-set decoding inside ker(R(b)) and ker(L(a)), the subspaces of vectors supported in one block that commute with every opposite-type check) found a weight-70 Z logical and a weight-84 X logical, both re-verified in-kernel and outside the stabilizer row space; stable through 40,000 ISD iterations with two seeds. Lowered to d_Z=70, d_X=84, d=70. Two-block codes are exactly the family this attack reaches, and uniform RIS does not see it." }, "family": "2bga-coset" }