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"date": "2026-10-12", "found_at_samples": 3000, "survived_samples": 200000, "tool": "ISD on codewords fixed by a central involution (g2bga_stop)" } } }, "provenance": { "authors": [ "@MicheldeMessieres" ], "construction": "Two-block group-algebra (2BGA) code, check weight 6, over G = C24 x Dic5 (order 480; Dic5 = C5 : C4 = , z of order 24 central). Element z^c x^i y^j is indexed 20c+4i+j; product (c1,i1,j1)(c2,i2,j2) = (c1+c2 mod 24, i1+(-1)^j1 i2 mod 5, j1+j2 mod 4). H_X=[L(a)|R(b)], H_Z=[R(b)^T|L(a)^T] with L(a)[g,h]=1 iff g=alpha h, R(b)[g,h]=1 iff g=h beta; qubits 0..479 = block 1, 480..959 = block 2. a={1, z^23 x^3 y, z^6 x^3}, b={1, z^10 x^3 y^3, z^4 x}. Found by an exhaustive symmetry-reduced census of weight-6 2BGA codes over C24 x Dic5 (two-sided translations and Aut(G) removed).", "origin": "submission", "novelty": "unknown", "model": "Claude Opus 5.5 (Claude Code)", "references": [ "arXiv:2306.16400", "arXiv:2305.06890" ], "date": "2026-10-12", "notes": "Our contribution: the choice of group C24 x Dic5 and the supports a, b, found by an exhaustive symmetry-reduced enumeration of weight-6 2BGA codes over this group, and the distance evidence (the 2BGA construction is Lin and Pryadko's, arXiv:2306.16400; see also Wang, Lin and Pryadko, arXiv:2305.06890). The stored witnesses (weight 40 on each side) are constant on the cosets of the central Klein four-group V = {1, z^12, y^2, z^12 y^2}: they are lifts of weight-10 logicals of the 240-qubit quotient code over G/V = C12 x D5, a standard way to get upper bounds for group codes (the same idea as the orbit stage of the board's verify/heuristic_distance.py). Distance is a witness-backed upper bound: no search found anything lighter than 40 (deepest: 200000 plain random-information-set trials per side followed by quotient searches); plain searches without the symmetry restriction found 46 (30000 trials per side), 52 (the board's verify/heuristic_distance.py, 100000 RIS + 8000000 fast trials, run with its orbit stage switched off on purpose to measure plain RIS) and 44 (the 8000000 fast trials of the board's deep gate, whose orbit stage also reports nothing lighter than 40). Literature novelty is unverified. Search direction inspired by codes/672-20-32.json by @vprusso (the weight-6 cell leader, over C_12 \u22ca_5 C_28 \u2245 C28 x Dic3) and continues our own codes/720-16-36.json (C18 x Dic5).", "search_budget": { "cpu_hours": 3.5, "ris_trials_per_side": 200000 } } }