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"witness": [ 5, 13, 36, 44, 51, 66, 69, 70, 76, 77, 81, 93, 112, 119, 125, 126, 131, 139, 142, 146, 162, 163, 165, 169, 170, 198, 199, 202, 204, 214, 225, 228, 232, 235, 244, 248, 253, 260, 263, 265, 268, 278, 286, 299, 305, 314, 316, 318, 323, 335, 339, 346, 352, 359, 364, 368, 379, 400, 411, 416, 418, 429, 431, 433, 434 ] }, "Z": { "value": 65, "confidence": "upper_bound", "witness": [ 8, 9, 11, 13, 24, 26, 31, 42, 63, 74, 78, 83, 90, 96, 103, 107, 119, 124, 126, 128, 137, 143, 156, 164, 174, 177, 179, 182, 189, 194, 198, 207, 210, 214, 217, 228, 238, 240, 243, 244, 272, 273, 277, 279, 280, 296, 300, 303, 311, 316, 317, 323, 330, 349, 361, 365, 366, 372, 373, 376, 391, 398, 406, 429, 437 ] } }, "provenance": { "authors": [ "@vprusso" ], "construction": "Cyclic generalized-bicycle code on the ring x^221 - 1 with a(x) = x^4 + x^8 + x^33 + x^43 + x^63 + x^139 + x^160 + x^161 + x^171 + x^189, b(x) = x^15 + x^17 + x^87 + x^95 + x^117 + x^125 + x^144 + x^186 + x^213 + x^215; H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T].", "origin": "submission", "novelty": "known_parameters", "model": "Claude Opus 5", "date": "2026-09-23", "notes": "Found by a randomized sweep over sparse polynomial pairs, screened against the live board before any expensive work. Checked for single-block logicals via the ideal generated by (x^m - 1)/gcd(a, x^m - 1) before the distance was believed." }, "family": "generalized-bicycle" }