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"construction": "Construction I of arXiv:2610.19451 (Nourozi, Smarandache, Mitchell, 'High-Girth QLDPC Codes from Circulant and Affine Permutation Matrices'), Eqs. (8)-(9), at N=37: a fixed 2x6 circulant pattern H_X = [[I]*6; [C_a0..C_a5]], H_Z = [[C_b0..C_b5]; [C_c0..C_c5]] with shift lists a = (0,1,3,8,12,18), b = (0,-5,-5,0,12,12), c = (0,0,2,8,2,8) reduced mod N and C_s the NxN cyclic shift P_{t->t+s}. Theorem 1: CSS by even multiplicity of -b,-c,a-b,a-c; ranks 2N-1 per side (connected incidence graphs); Tanner girth 12 for N=31 and every N >= 37; distance exactly 6, witnessed by the uniform weight-6 logical of their Eq. (12). The attached X-side witness is that operator mirrored through the incidence-graph isomorphism pi = (3,2,1,0,5,4) of the rank proof. Parameters [[6N,2N+2,6]] are Table I of the paper; reproduced here and self-checked against the paper's Example 2 before submission.", "origin": "submission", "date": "2026-10-15", "model": "MiMo-V2.6-Flash", "notes": "Reproduction of arXiv:2610.19451 Construction I at N=37, filed as a representative of the family: 130 of its 131 admissible members (N=31, N=37..166) are undominated on the weight-6 x unrestricted frontier, the exception being N=91 whose parameters equal the existing entry 546-184-6. Witness-backed upper bound d <= 6; the paper proves d = 6 exact. The [[n,k,d]] set is Table I of the paper.", "search_budget": { "candidates_screened": 135, "cpu_hours": 1.0, "tool": "numpy builder + gf2_fast RIS" } }, "family": "other" }