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depth 8)", "survived_samples": 183000000 } }, "Z": { "value": 34, "confidence": "upper_bound", "witness": [ 23, 29, 48, 77, 90, 96, 102, 150, 202, 210, 227, 239, 245, 306, 347, 353, 360, 397, 403, 416, 422, 428, 451, 470, 499, 530, 613, 619, 630, 644, 698, 721, 727, 746 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-23", "found_at_samples": 5000000, "seeds": [ 23000031601 ], "tool": "GPU sketch k_sub 256 (recover), screen stage 3", "survived_samples": 183000000 } } }, "family": "generalized-bicycle", "provenance": { "authors": [ "@vprusso" ], "origin": "submission", "novelty": "new_parameters", "model": "Claude Fable 5.1 (Claude Code)", "construction": "Two-block group-algebra code over the metacyclic group Z_21 x| Z_18 with r = 4 (research/kit/group_algebra.py metacyclic(21, 18, 4) and build_2bga, element index i*18 + j for x^i y^j with y x y^-1 = x^4): a = [36, 173, 376, 131], b = [146, 364, 27, 225] as element indices, H_X = [L(a) | R(b)], H_Z = [R(b)^T | L(a)^T] with L, R the left and right regular representations. n = 2|G| = 756, k = 24, every check has weight 8.", "references": [ "arXiv:2306.16400", "arXiv:2111.03654" ], "date": "2026-09-23", "notes": "Found by a GPU random-information-set screen (deep kernel: full-basis RREF plus pair sums) over metacyclic two-block group-algebra codes with weight-4 supports at n in [702, 1000]; see the research note for the ladder. Lightest logicals: X 34, Z 34; deep-kernel GPU passes (full basis, pair depth 8): X 34 at 20,000,000 trials (seed 2101); Z 34 at 20,000,000 trials (seed 2101); X 34 at 100,000,000 trials (seed 2102); Z 34 at 100,000,000 trials (seed 2102); board fast pass 34 at 8,000,000 trials. Every operator re-verified with verify/gf2.py. Distance is a witness-backed upper bound. Novelty: no isomorphic code found by a nauty canonical-form check against the board and the 2BGA, GB, BB, QECDB, and codetables data (submitter claim). Generator spec: {\"family\": \"2bga-metacyclic\", \"n\": 21, \"k_m\": 18, \"r\": 4, \"a\": [36, 173, 376, 131], \"b\": [146, 364, 27, 225]}" } }