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141, 207, 517, 553, 573 ], [ 2, 142, 216, 435, 487, 574 ], [ 27, 143, 265, 461, 506, 575 ] ] }, "distance": { "d": 30, "X": { "value": 30, "confidence": "upper_bound", "witness": [ 0, 12, 19, 46, 60, 61, 117, 120, 147, 162, 163, 167, 192, 196, 231, 301, 305, 317, 332, 340, 378, 400, 416, 419, 421, 422, 431, 432, 441, 444 ] }, "Z": { "value": 30, "confidence": "upper_bound", "witness": [ 42, 69, 101, 158, 165, 166, 168, 183, 211, 221, 236, 243, 254, 294, 312, 345, 357, 389, 409, 414, 427, 430, 436, 456, 474, 489, 493, 517, 518, 552 ] } }, "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(432,692) (GAP SmallGroups id), H = = C3 given by generators in the polycyclic generating sequence f1,f2,... of G, m = [G:H] = 144, n = 4m = 576. 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 + f2*f4*f5^2*f6 + f1*f4*f5*f6^2*f7; B = [[1, 1 + f3*f4*f6*f7^2], [1 + f3*f7^2, f6^2*f7^2]]. Rebuild with gap/rebuild.g in https://github.com/rajendrarajpurohit/CLP_QLDPC.", "origin": "submission", "date": "2026-10-30", "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.", "model": "human" }, "family": "2bga-coset" }