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"authors": [ "@vprusso" ], "construction": "Periodic bivariate-bicycle code on Z_31 x Z_9 (n = 2*l*m = 558): x = S_31 tensor I_9, y = I_31 tensor S_9 (cyclic shifts), qubit index i*m + j in each block; A = x^0y^0 + x^4y^2 + x^18y^5 + x^30y^1, B = x^0y^0 + x^3y^4 + x^19y^0 + x^23y^6; H_X = [A|B], H_Z = [B^T|A^T] (research/kit/bb.py build_bb(31, 9, [[0, 0], [4, 2], [18, 5], [30, 1]], [[0, 0], [3, 4], [19, 0], [23, 6]])). gcd(31, 9) = 1, so Z_31 x Z_9 is cyclic of order 279 and the code is the cyclic generalized-bicycle code over Z_279 with a(z) = z^0 + z^128 + z^154 + z^266, b(z) = z^0 + z^81 + z^220 + z^240 (CRT relabeling x^a y^b -> z^t, t = a mod 31, t = b mod 9).", "date": "2026-09-26", "notes": "Found by the fourth LER-objective search (coprime bivariate-bicycle codes (gcd(l, m) = 1) with check weight 6, 7, or 8 at 420 < n <= 700 and k >= 8): circuit-level logical error rate at 3 rounds under the board's depolarizing recipe, interleaved schedule, decoded with CUDA-Q QEC nv-qldpc-decoder (BP+OSD-CS order 10). At p = 0.002, 100000 shots per basis: Z memory 5 failures, X memory 10 failures, against 12 copies of the distance-7 rotated surface code (1164 physical qubits, same builder and decoder) with 87 and 87 failures. Decoder-based d_circ estimate at 3 rounds: 118. Distance: RIS at 20,000 trials (gf2_fast) and a 300,000,000-trial verify/ris_gpu.py pass per side; upper bounds. A norm-lift quotient bound over the divisors of m and a single-block kernel bound were run before admission (lightest lift 45). Details in the accompanying note.", "model": "Claude Fable 5.1 (Claude Code)", "origin": "submission", "novelty": "unknown" } }