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"upper_bound", "witness": [ 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167 ] } }, "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 + y^3, B = 1 + x y^3 + x^4 y^8, lattice (15,14), taken from Table 3 of arXiv:2610.06623v1 (class CL-576cc4f9). The paper's catalogue carried only a raw BP-OSD-family decoder scalar for this row (no persisted witness) and no exact certificate. The distance claimed here is an upper bound from an independent witness search, not the paper's raw decoder scalar. Construction and distance witness 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-576cc4f9. This entry is an independent reconstruction and re-measurement, not a new construction. 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-14 logical operator on each side (zero syndrome, outside the stabilizer row space, re-confirmed by a second, independent exclusion check), confirming the paper's decoder scalar holds rather than collapsing. The paper prints three more BLISS-confirmed non-isomorphic (15,14) presentations at this same [[420,8,14]] point (class CL-5e7d0343: A = 1 + y^11, B = 1 + x^11 y^11 + x^14 y^13; class CL-e2918556: A = 1 + y, B = 1 + x^3 y^4 + x^4 y^9; class CL-eb460c33: A = 1 + y, B = 1 + x y^5 + x^12 y^3), all independently hardened to the same weight-14 bound by the same search; none is filed as a separate board entry since none would advance any new frontier cell.", "references": [ "arXiv:2610.06623v1" ] }, "family": "bivariate-bicycle" }