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212, 213, 220, 222, 232, 247, 248, 254, 255, 259, 265, 267, 283, 293, 298, 300, 304, 310, 314, 336, 347, 350, 355, 356, 357, 360, 366, 367, 373, 376, 388, 408, 417, 418, 430, 431, 435, 451, 457, 464, 467, 472, 488, 489, 491, 492, 496, 501, 514, 515, 516, 547, 557, 558, 561, 567, 570, 574, 589, 593, 608, 617, 629, 631, 636, 637, 643, 650, 652, 655, 661, 666, 676, 678 ] } }, "provenance": { "authors": [ "@Ming-yuan-Liang" ], "construction": "Kasai affine 2BGA: a two-block group-algebra code over the affine group Aff(F_q) in its metacyclic realization Z_q x| Z_{q-1} (order q(q-1); 342 for q=19, 272 for q=17). With research/kit/group_algebra.py: mul, _ = metacyclic(q, q-1, r) where r is the smallest primitive root mod q, then HX, HZ = build_2bga(mul, a, b) for the two exponent sets a, b recorded in the reproduction section.", "references": [], "date": "2026-10-27", "notes": "Checked against the board at the gate: no exact-fingerprint or WL-signature collision (gates.dedup reports neither), so the entry is declared not equivalent to any existing entry.", "model": "GLM-5.3-Flash", "origin": "submission", "search_budget": { "candidates_screened": 300, "wall_clock_hours": 11, "tool": "research/kit search lanes (numpy RIS surrogate, 400-trial screen; fresh-seed 20,000-trial confirmation rungs)", "ris_trials_per_side": 20000 } }, "family": "generalized-bicycle" }