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"GPU deep kernel (full basis, pair depth 8), screen stage 3", "survived_samples": 60000000 } } }, "family": "generalized-bicycle", "provenance": { "authors": [ "@vprusso" ], "origin": "submission", "novelty": "new_parameters", "construction": "Cyclic (single-circulant-pair) generalized-bicycle code over Z_217 (research/cyclic_gb.py build_cyclic_gb): a(x) = 1 + x^18 + x^110, b(x) = 1 + x^10 + x^99; H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T] with circ(v)[i, (i + j) mod 217] = v[j]. n = 2m = 434, k = 2 deg gcd(a, b, x^217 - 1) = 16, every check has weight 6. a and b were drawn as weight-3 multiples of a degree-8 divisor g of x^217 - 1 (g as a little-endian bit integer: 307).", "references": [ "arXiv:1904.02703", "arXiv:2203.17216" ], "date": "2026-09-23", "model": "Claude Fable 5.1 (Claude Code)", "notes": "Found by a GPU random-information-set screen (verify/ris_gpu.cu deep kernel: full-basis RREF plus pair sums, pair depth 8) over weight-6 cyclic generalized-bicycle codes with weight-3 polynomials at n <= 700; see the research note for the ladder. Lightest logicals: X 22, Z 22; finalist deep-kernel GPU pass: X 22 at 50,000,000 trials (seed 777); Z 22 at 50,000,000 trials (seed 778); board fast pass 22 at 8,000,000 trials. Every operator re-verified with verify/gf2.py. Distance is a witness-backed upper bound. Novelty: new_parameters by a nauty canonical-form check of the typed Tanner graph against the board and the 2BGA, GB, BB, QECDB, and codetables data (a submitter claim). Generator spec: {\"family\": \"cyclic-gb\", \"m\": 217, \"g_int\": 307, \"deg_g\": 8, \"a\": [0, 18, 110], \"b\": [0, 10, 99]}" } }