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135, 144, 165, 168, 180, 184, 241, 243, 258, 276, 279, 282, 298, 301, 302, 330, 335, 336, 356, 357, 360, 361, 376, 381, 394, 396, 402, 410, 420, 427 ], "witness_provenance": { "found_by": [ "@rajendrarajpurohit" ], "date": "2026-11-03", "found_at_samples": 1, "survived_samples": 1, "tool": "verify/gate_changed.py (CI gate of PR #4477, orbit-fold search, seed 1516409015)", "seeds": [ 1516409015 ] } }, "Z": { "value": 40, "confidence": "upper_bound", "witness": [ 21, 96, 130, 229, 236, 255, 266, 282, 297, 305, 311, 329, 342, 354, 356, 377, 385, 395, 407, 413, 426, 441, 453, 478, 487, 501, 513, 528, 606, 632, 657, 680, 694, 706, 717, 719, 751, 754, 786, 836 ] } }, "provenance": { "authors": [ "@rajendrarajpurohit" ], "construction": "Coset lifted product (CLP) code, Definition III.1 of arXiv:2610.12782, 1x1 over 2x2 layout, check weight 6. G = SmallGroup(648,720) (GAP SmallGroups id), H = = C3 given by generators in the polycyclic generating sequence f1,f2,... of G, m = [G:H] = 216, n = 4m = 864. Protograph a over F_2[G] acts by the left coset action on G/H, protograph B over F_2[N_G(H)] by the right coset action. a = 1 + f1*f3*f4*f5*f6*f7 + f1*f2*f3^2*f5*f7; B = [[1, 1 + f1*f3^2*f4*f5^2*f7], [1 + f1*f3^2*f4*f5*f7, f1*f3^2*f4*f5^2]]. Rebuild with gap/rebuild.g in https://github.com/rajendrarajpurohit/CLP_QLDPC.", "origin": "submission", "date": "2026-11-01", "search_budget": { "ris_trials_per_side": 500000 }, "references": [ "arXiv:2610.12782" ], "novelty": "new_parameters", "notes": "New parameter set, not in arXiv:2610.12782. Found by the paper's search procedure extended from m <= 100 to 120 <= m <= 250 (pairs (G,H) with H cyclic, core free, [G:N_G(H)] in {2,3,4}), weight 6 shape |a| = 3 with B entry weights 2 1 / 1 2 or 1 2 / 2 1. Screened with QDistRnd, 10^6 rounds per side; the witness here is from this tool's own RIS search. Authors Rajendra Rajpurohit, V. Lalitha, Shayan Srinivasa Garani. The CI gate of PR #4477 found a weight 36 logical (orbit-fold search); the claim was lowered from 40 to 36 and that witness is the one carried on that side.", "model": "human" }, "family": "2bga-coset" }