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319, 365, 406, 443, 481, 566, 577 ], [ 6, 108, 109, 168, 225, 268, 292, 320, 366, 407, 444, 482, 567, 578 ], [ 7, 109, 110, 169, 226, 269, 293, 321, 367, 408, 445, 483, 568, 579 ], [ 8, 110, 111, 170, 227, 270, 294, 322, 368, 409, 446, 484, 569, 580 ] ] }, "distance": { "d": 30, "X": { "value": 30, "confidence": "upper_bound", "witness": [ 2, 23, 44, 65, 86, 107, 128, 149, 170, 191, 212, 233, 254, 275, 296, 322, 343, 364, 385, 406, 427, 448, 469, 490, 511, 532, 553, 574, 595, 616 ] }, "Z": { "value": 30, "confidence": "upper_bound", "witness": [ 14, 35, 56, 77, 98, 119, 140, 161, 182, 203, 224, 245, 266, 287, 308, 334, 355, 376, 397, 418, 439, 460, 481, 502, 523, 544, 565, 586, 607, 628 ] } }, "provenance": { "authors": [ "@vprusso" ], "construction": "Cyclic generalized-bicycle code on the ring x^315 - 1 with a(x) = x^49 + x^60 + x^145 + x^183 + x^220 + x^261 + x^307, b(x) = x^20 + x^44 + x^87 + x^144 + x^203 + x^204 + x^306; H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T].", "origin": "submission", "novelty": "known_parameters", "model": "Claude Opus 5", "date": "2026-09-27", "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" }