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300, 319, 348, 368, 388, 427, 434, 436, 437, 474 ] } }, "provenance": { "authors": [ "@TimoKellerMath" ], "origin": "submission", "novelty": "known_parameters", "construction": "Cyclic two-block (generalized bicycle) code over Z_252: H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T] with circ(v)[i, (i + j) mod 252] = v[j]; a(x) = 1 + x + x^58, b(x) = 1 + x^48 + x^166. n = 504, k = 12 (= 2 ord_63(2): the code captures one reduced point of order 63, a common zero of a and b in mu_63), check weight 6, qubit degree 6.", "references": [ "arXiv:1904.02703", "arXiv:2306.16400", "arXiv:2511.13560" ], "date": "2026-11-10", "model": "Claude Opus 5.5", "notes": "Exact distance: d_X = d_Z = 28, proved by an exhaustive anchored search at W = 26 with two independently written programs, the X/Z exchange (block 1, i) <-> (block 2, -i), and the parity of ker H_X; see the research note and certs/504-12-28.json. Novelty: no [[504,12]] entry on the board (commit 8042f9da). Symons, Rajput and Browne (arXiv:2511.13560, Table 1) list a different weight-6 bivariate bicycle code with n = 504, k = 12 and d <= 30 from BP-OSD; by our computation its distance is also 28 (not part of this submission), so the parameters [[504,12,28]] are those of a published code; this entry adds a cyclic construction and the exact distance." }, "family": "generalized-bicycle" }