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901 ] ] }, "distance": { "d": 38, "X": { "value": 38, "confidence": "upper_bound", "witness": [ 15, 29, 62, 89, 96, 130, 137, 171, 190, 212, 217, 231, 264, 318, 325, 365, 372, 400, 419, 439, 447, 476, 480, 492, 533, 545, 598, 614, 651, 667, 685, 726, 752, 791, 793, 858, 860, 890 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-23", "found_at_samples": 60000000, "seeds": [ 2102 ], "tool": "GPU deep kernel (full basis, pair depth 8)", "survived_samples": 143000000 } }, "Z": { "value": 38, "confidence": "upper_bound", "witness": [ 10, 47, 94, 95, 111, 148, 164, 217, 229, 252, 270, 286, 299, 353, 355, 420, 422, 461, 475, 498, 531, 545, 550, 572, 591, 625, 632, 673, 700, 721, 747, 766, 794, 813, 841, 848, 888, 895 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-23", "found_at_samples": 20000000, "seeds": [ 2101 ], "tool": "GPU deep kernel (full basis, pair depth 8)", "survived_samples": 143000000 } } }, "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_451 (research/cyclic_gb.py build_cyclic_gb): a(x) = 1 + x^53 + x^246 + x^313, b(x) = 1 + x^41 + x^229 + x^276; H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T] with circ(v)[i, (i + j) mod 451] = v[j]. n = 2m = 902, k = 2 deg gcd(a, b, x^451 - 1) = 42, every check has weight 8. a and b were drawn as weight-4 multiples of a degree-21 divisor g of x^451 - 1 (g as a little-endian bit integer: 4044695).", "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 38, Z 38; deep-kernel GPU passes (full basis, pair depth 8): X 40 at 20,000,000 trials (seed 2101); Z 38 at 20,000,000 trials (seed 2101); X 38 at 60,000,000 trials (seed 2102); Z 38 at 60,000,000 trials (seed 2102); board fast pass 38 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\": \"cyclic-gb\", \"m\": 451, \"g_int\": 4044695, \"deg_g\": 21, \"a\": [0, 53, 246, 313], \"b\": [0, 41, 229, 276]}" } }