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271, 279, 280, 282, 286, 294, 295, 297, 301, 309, 310, 312 ] }, "Z": { "value": 84, "confidence": "upper_bound", "witness": [ 318, 320, 321, 329, 333, 335, 336, 344, 348, 350, 351, 359, 363, 365, 366, 374, 378, 380, 381, 389, 393, 395, 396, 404, 408, 410, 411, 419, 423, 425, 426, 434, 438, 440, 441, 449, 453, 455, 456, 464, 468, 470, 471, 479, 483, 485, 486, 494, 498, 500, 501, 509, 513, 515, 516, 524, 528, 530, 531, 539, 543, 545, 546, 554, 558, 560, 561, 569, 573, 575, 576, 584, 588, 590, 591, 599, 603, 605, 606, 614, 618, 620, 621, 629 ] } }, "provenance": { "authors": [ "@vprusso" ], "construction": "Cyclic generalized-bicycle code on the ring x^315 - 1 with a(x) = x^3 + x^79 + x^116 + x^167 + x^231 + x^250 + x^281, b(x) = x^0 + x^18 + x^62 + x^64 + x^78 + x^87 + x^123 + x^139 + x^157 + x^158 + x^171 + x^190 + x^219 + x^300 + x^313; H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T].", "origin": "submission", "novelty": "known_parameters", "model": "Claude Opus 5", "date": "2026-09-26", "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" }