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"provenance": { "authors": [ "@vprusso" ], "construction": "Periodic bivariate-bicycle code on Z_27 x Z_7 (n = 2*l*m = 378): x = S_27 tensor I_7, y = I_27 tensor S_7 (cyclic shifts), qubit index i*m + j in each block; A = x^0y^0 + x^1y^2 + x^25y^1, B = x^0y^0 + x^12y^5 + x^17y^1 + x^19y^2; H_X = [A|B], H_Z = [B^T|A^T] (research/kit/bb.py build_bb(27, 7, [[0, 0], [1, 2], [25, 1]], [[0, 0], [12, 5], [17, 1], [19, 2]])). gcd(27, 7) = 1, so Z_27 x Z_7 is cyclic of order 189 and the code is the cyclic generalized-bicycle code over Z_189 with a(z) = z^0 + z^106 + z^163, b(z) = z^0 + z^12 + z^71 + z^100 (CRT relabeling x^a y^b -> z^t, t = a mod 27, t = b mod 7).", "date": "2026-09-25", "notes": "Found by the third LER-objective search (weight-6 and weight-7 two-block codes at 300 < n <= 420 with k >= 12): 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 9 failures, X memory 3 failures, against 12 copies of the distance-7 rotated surface code (1164 physical qubits, same builder and decoder) with 101 and 88 failures. Decoder-based d_circ estimate at 3 rounds: 58. Distance: RIS at 20,000 trials (gf2_fast) and a 300,000,000-trial verify/ris_gpu.py pass per side; upper bounds. Details in the accompanying note.", "origin": "submission", "novelty": "unknown", "model": "Claude Fable 5.1 (Claude Code)" } }