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"date": "2026-11-06", "found_at_samples": 1, "survived_samples": 1, "tool": "verify/heuristic_distance.py orbit-fold, 3000 trials, seed 1", "seeds": [ 1 ] } } }, "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(480,1005) (GAP SmallGroups id), H = = C2 given by generators in the polycyclic generating sequence f1,f2,... of G, m = [G:H] = 240, n = 4m = 960. 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*f6^2*f7^4 + f1*f2*f3*f4*f6^2*f7; B = [[1 + f4*f5*f6*f7^3, 1], [1, f4*f5*f6 + f4*f6*f7^2]]. Rebuild with gap/rebuild.g in https://github.com/rajendrarajpurohit/CLP_QLDPC.", "origin": "submission", "date": "2026-11-06", "search_budget": { "ris_trials_per_side": 500000 }, "references": [ "arXiv:2610.12782" ], "novelty": "new_parameters", "notes": "Neighbour of the W6rest m = 240 family of arXiv:2610.12782 found by the entry-resampling walker (mut960 campaign, check weight 6, both sides screened at search time). Search-time QDistRnd bound d <= 56. This repository's fast RIS search at 8M trials (seed 6980315) found nothing below 42 on either side; the orbit-fold search (pynauty automorphisms) found weight 42 at 300 trials and a weight-40 Z-type logical at 3000 trials (seed 1), carried as the witness; 30000 fold trials found nothing lighter. The X side carries its weight-42 witness. Classical construction: a coset lifted product code in the framework of arXiv:2610.12782 (Definition III.1), obtained by the search procedure described in that paper over the GAP SmallGroups library. No AI model. No entry at check weight 6 with n <= 960 and k >= 20 reaches d = 40 on the current board.", "model": "human" }, "family": "2bga-coset" }