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298, 335, 573 ], [ 6, 104, 286, 305, 312, 574 ], [ 7, 105, 287, 288, 313, 575 ] ] }, "distance": { "d": 20, "X": { "value": 20, "confidence": "upper_bound", "witness": [ 9, 21, 29, 87, 119, 127, 159, 179, 191, 265, 387, 393, 399, 418, 424, 430, 437, 455, 456, 487 ] }, "Z": { "value": 20, "confidence": "upper_bound", "witness": [ 50, 68, 75, 93, 106, 118, 137, 143, 150, 156, 298, 330, 364, 396, 416, 428, 448, 456, 514, 534 ] } }, "provenance": { "authors": [ "@mathysrennela" ], "construction": "Construction II of arXiv:2610.19451 (Nourozi, Smarandache, Mitchell, 'High-Girth QLDPC Codes from Circulant and Affine Permutation Matrices'), Section IV Theorem 2, outer lift q=6: fixed polynomials A(z) = [[I+zC2, zF],[F, I+zC2]] and B(z) = [[I, zC8+z^3C10],[C8+z^2C22, I]] of 2x2 blocks of Z_24 circulants and the affine permutation F = F_(7,7) (t -> 7t+7); the lift sends z^h M_h to S_q^h (x) M_h with S_q the qxq cyclic shift, and H_X = [A_q | B_q], H_Z = [B_q^T | A_q^T]. The polynomial identity AB = BA (via F C_s = C_(7s) F) guarantees CSS orthogonality at every lift size; checks are row weight 6, column weight 3, Tanner girth 8, ranks 272 per side (k = 32). Table II certifies d = 20 exact by bounded enumeration but publishes no operators, so the attached weight-20 witnesses are upper bounds found here: the submission tool's own search (20000 numpy RIS trials plus 2000000 accelerator trials, seed 0), after an escalating pre-screening ladder (gf2_fast, pair depth 8; 200k trials seed 101 through 2M seed 104, plus a numpy pass 8000 trials seed 999) had already read 20 on both sides. Of the paper's four tabulated lifts, only q=6 is undominated on the board (q=2,3,4 lose to existing 192-16-12, 288-16-16, 240-16-14/360-20-20). Self-checked against the paper's Example 3 row support, Example 4 logical, and Table II ranks before submission.", "origin": "submission", "date": "2026-10-16", "model": "MiMo-V2.6-Flash", "notes": "Reproduction of arXiv:2610.19451 Construction II at q=6, the only one of the paper's four tabulated lifts not dominated on the board; it advances weight-6 x unrestricted on n, k and d (nothing at n <= 576 holds k >= 32 with d >= 20 at w <= 6) and matches the baseline entry 360-20-20's kd^2/n = 22.22 at double the logical qubits. Witness-backed upper bound d <= 20 on both sides; the paper certifies d = 20 exact but does not publish the operators, so these were found by a RIS ladder. The [[n,k,d]] set is Table II of the paper.", "search_budget": { "candidates_screened": 135, "ris_trials_per_side": 3400000, "cpu_hours": 6.0, "tool": "numpy builder + gf2_fast RIS ladder" } }, "family": "generalized-bicycle" }