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"upper_bound", "witness": [ 7, 9, 42, 56, 58, 105, 119, 121, 140, 154, 156, 203, 301, 309, 313, 317 ] } }, "provenance": { "authors": [ "@cbjuan" ], "construction": "Bivariate bicycle code over F_2[x,y]/(x^15-1, y^14-1) with mixed-monomial weight-five polynomials A = 1 + x^4 y^7, B = 1 + x^14 y^2 + x^14 y^6, lattice (15,14), taken from Table 3 of arXiv:2610.06623v1. The paper reports this presentation with the interval 5 <= d <= 16 (evidence L4+I) and no exact certificate. The distance claimed here is an upper bound from this repository's own witness search, not the paper's interval endpoint. Construction and distance witnesses by Juan Cruz-Benito (@cbjuan).", "origin": "submission", "date": "2026-10-07", "model": "human", "notes": "Known parameters: the (n,k,d) triple and the explicit polynomial presentation are published in arXiv:2610.06623v1, Table 3, class CL-dcca76b0. This entry is an independent reconstruction and re-measurement, not a new construction. The paper's own catalogue carried only an unverified MILP-incumbent (I-tier) upper bound for this row, with no independent witness search performed; this repository's own prior experience is that such bounds can collapse under scrutiny (9 of 10 audited B-tier bounds in the same campaign did). An independent randomized GF(2) kernel/permutation witness search (8,000 trials/side) rebuilt the check matrices from the published polynomials and found a weight-16 logical operator on each side, confirming the paper's upper bound holds rather than collapsing. k was independently re-derived as rank(H_X)+rank(H_Z) subtracted from n, matching the paper's k=6.", "references": [ "arXiv:2610.06623v1" ] }, "family": "bivariate-bicycle" }