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"witness": [ 1, 3, 16, 19, 21, 30, 41, 48, 77, 90, 110, 111, 113, 115, 135, 142, 167, 196, 205, 221, 230, 246, 271, 277, 285, 300 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-23", "found_at_samples": 50000000, "seeds": [ 777 ], "tool": "GPU sketch k_sub 161", "survived_samples": 178000000 } }, "Z": { "value": 26, "confidence": "upper_bound", "witness": [ 2, 15, 17, 22, 32, 40, 46, 47, 63, 72, 76, 92, 116, 130, 139, 166, 172, 177, 198, 218, 236, 240, 265, 271, 274, 303 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-23", "found_at_samples": 50000000, "seeds": [ 778 ], "tool": "GPU sketch k_sub 161", "survived_samples": 178000000 } } }, "family": "generalized-bicycle", "provenance": { "authors": [ "@vprusso" ], "origin": "submission", "novelty": "new_parameters", "model": "Claude Fable 5.1 (Claude Code)", "construction": "Cyclic (single-circulant-pair) generalized-bicycle code over Z_155 (research/cyclic_gb.py build_cyclic_gb): a(x) = 1 + x^11 + x^25 + x^40, b(x) = 1 + x^20 + x^81 + x^126; H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T] with circ(v)[i, (i + j) mod 155] = v[j]. n = 2m = 310, k = 2 deg gcd(a, b, x^155 - 1) = 12, every check has weight 8. Taken as one connected component of the Z_465 code with a = 1 + x^33 + x^75 + x^120, b = 1 + x^60 + x^243 + x^378 (all offsets divisible by 3), which is the direct sum of three copies of this code.", "references": [ "arXiv:1212.6703", "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 cyclic generalized-bicycle codes with weight-4 polynomials at n in [702, 1000]; see the research note for the ladder. Lightest logicals: X 26, Z 26; deep-kernel GPU passes (full basis, pair depth 8): X 26 at 20,000,000 trials (seed 2101); Z 26 at 20,000,000 trials (seed 2101); X 26 at 100,000,000 trials (seed 2102); Z 26 at 100,000,000 trials (seed 2102); board fast pass 26 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). One connected component of the Z_465 direct sum described in the construction. Generator spec: {\"family\": \"cyclic-gb\", \"m\": 155, \"g_int\": null, \"deg_g\": null, \"a\": [0, 11, 25, 40], \"b\": [0, 20, 81, 126], \"component_of\": \"[[930,36,26]] pod1B/cyclicgb-w8-s13 batch 0\"}" } }