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351, 387 ], [ 8, 18, 24, 60, 91, 111, 163, 169, 211, 249, 288, 297, 302, 304, 352, 388 ], [ 9, 19, 25, 61, 92, 112, 164, 170, 212, 250, 289, 298, 303, 305, 353, 389 ] ] }, "distance": { "d": 27, "X": { "value": 27, "confidence": "upper_bound", "witness": [ 2, 8, 18, 24, 36, 52, 59, 70, 74, 126, 128, 132, 145, 146, 148, 207, 211, 214, 239, 245, 265, 266, 284, 289, 300, 303, 386 ] }, "Z": { "value": 35, "confidence": "upper_bound", "witness": [ 3, 14, 34, 40, 53, 68, 114, 121, 135, 137, 139, 143, 184, 202, 220, 225, 226, 231, 233, 239, 253, 260, 272, 275, 281, 310, 316, 317, 320, 324, 346, 368, 372, 382, 383 ] } }, "provenance": { "authors": [ "@seunomonije" ], "model": "Claude Fable 5", "construction": "Generalized bicycle (two-block) code on the cyclic group Z_195: H_X = [A|B], H_Z = [B^T|A^T] with A, B circulants; a(x) support {0,36,84,86,91,100,139,177}, b(x) support {24,30,82,102,133,169,175,185}. Both a and b are sparse multiples of a degree-37 divisor g of x^195-1 (product of the degree-1 factor x+1 and three degree-12 irreducible factors), giving k = 2*deg gcd(a,b,x^195-1) = 82 at n = 390 with weight-16 checks. Distance evidence: rising RIS ladder to 20M trials/side plus three independent 8M-trial refutation passes (seeds 777/888/999) all bottoming at d<=27; BP+OSD decoder search found nothing lighter than 46.", "references": [ "arXiv:1904.02703", "arXiv:2203.17216" ], "date": "2026-07-14", "notes": "Search and verification by Claude Fable 5 (model: Claude Fable 5)." }, "family": "generalized-bicycle" }