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44, 54, 80, 86, 93, 126, 159, 163, 176, 178, 179, 183, 221, 319, 328, 353, 355, 375, 411, 453, 464, 471, 522, 525, 531, 554 ] ] }, "distance": { "d": 88, "X": { "value": 88, "confidence": "upper_bound", "witness": [ 6, 11, 27, 40, 44, 52, 54, 66, 75, 81, 93, 102, 104, 105, 117, 121, 130, 131, 134, 141, 148, 151, 152, 158, 164, 169, 170, 173, 176, 178, 182, 191, 199, 203, 217, 220, 234, 249, 254, 267, 269, 280, 285, 290, 301, 312, 317, 320, 322, 323, 346, 362, 365, 374, 376, 393, 396, 397, 408, 409, 415, 417, 421, 424, 434, 438, 441, 444, 445, 449, 450, 452, 467, 468, 470, 472, 488, 491, 495, 498, 507, 535, 536, 538, 541, 545, 549, 556 ] }, "Z": { "value": 88, "confidence": "upper_bound", "witness": [ 0, 14, 21, 25, 29, 32, 34, 35, 63, 72, 75, 79, 82, 98, 100, 102, 103, 118, 120, 121, 125, 126, 129, 132, 136, 146, 149, 153, 155, 161, 162, 173, 174, 177, 194, 196, 205, 208, 224, 247, 248, 250, 253, 258, 269, 280, 290, 301, 303, 316, 321, 336, 350, 353, 367, 371, 379, 388, 392, 394, 397, 400, 401, 406, 412, 418, 419, 422, 429, 436, 439, 440, 449, 453, 465, 466, 468, 477, 489, 495, 504, 516, 518, 526, 530, 543, 559, 564 ] } }, "provenance": { "authors": [ "@vprusso" ], "construction": "Cyclic generalized-bicycle code on the ring x^285 - 1 with a(x) = x^15 + x^38 + x^44 + x^47 + x^98 + x^105 + x^116 + x^158 + x^194 + x^214 + x^216 + x^241 + x^250, b(x) = x^63 + x^101 + x^105 + x^106 + x^108 + x^121 + x^125 + x^158 + x^191 + x^198 + x^204 + x^230 + x^240 + x^241 + x^257 + x^260 + x^277 + x^282 + x^283; H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T].", "origin": "submission", "novelty": "known_parameters", "model": "Claude Opus 5", "date": "2026-09-24", "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" }