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 },
 "distance": {
  "d": 15,
  "X": {
   "value": 15,
   "confidence": "upper_bound",
   "witness": [
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   ]
  },
  "Z": {
   "value": 15,
   "confidence": "upper_bound",
   "witness": [
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   ]
  }
 },
 "provenance": {
  "authors": [
   "@cbjuan"
  ],
  "construction": "Bivariate bicycle code over F_2[x,y]/(x^18-1, y^12-1) with mixed-monomial weight-five polynomials A = 1 + x^4 y^6, B = 1 + x y^5 + x^5 y^10, lattice (18,12), taken from Table 3 of arXiv:2610.06623v1. The paper reports this presentation with the interval 5 <= d <= 15 (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-ab07a1d1. 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. 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-15 logical operator on each side, confirming the paper's upper bound holds. k was independently re-derived from the rebuilt check matrices, matching the paper's k=8.",
  "references": [
   "arXiv:2610.06623v1"
  ]
 },
 "family": "bivariate-bicycle"
}