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 },
 "distance": {
  "d": 20,
  "X": {
   "value": 20,
   "confidence": "upper_bound",
   "witness": [
    1,
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    19,
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   ]
  },
  "Z": {
   "value": 20,
   "confidence": "upper_bound",
   "witness": [
    12,
    28,
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   ]
  }
 },
 "provenance": {
  "authors": [
   "Cruz-Benito, Juan",
   "Cross, Andrew W.",
   "Kremer, David",
   "Faro, Ismael"
  ],
  "construction": "Bivariate bicycle code on Z_18 x Z_8 (l=18, m=8): A = 1 + x y^4 + x^14 y, B = 1 + x y^2 + x^2 y^7, H_X = [A | B], H_Z = [B^T | A^T], x = S_18 (x) I_8, y = I_18 (x) S_8, qubit index i*8 + j for cell (i, j). Catalog class Y, (18,8), mixed-monomial Campaign 4 of arXiv:2606.02418; rebuilt with research/kit/bb.py.",
  "references": [
   "arXiv:2606.02418"
  ],
  "date": "2026",
  "notes": "Literature baseline, seeded 2026-09-17. Listed in the CSS catalog of arXiv:2606.02418 (n = 288 table, class Y, (l, m) = (18, 8), mixed-monomial Campaign 4) at d = 20, kd^2/n = 11.1. The catalog's per-code records (github.com/qiskit-community/qcode-discovery @ d12bea2c, results/campaign4_milp_verified.jsonl and results/campaign4_reverified.jsonl) mark this distance a MILP incumbent rather than proven optimal: all 16 logicals returned weight-20 incumbents at 300 s and again at 3000 s per logical, and the authors' 300k-trial BP-OSD attack found nothing lighter. Recorded here as a witness-backed upper bound (d <= 20 on both sides: weight-20 logicals found by the kit at 4000 RIS trials per side, and 3 x 1M accelerator trials found nothing lighter) pending this repo's own server certification. Reproduction validated: research/kit/bb.py with the listed exponents reproduces the catalog's check matrices row for row. In the unrestricted weight-6 cells this baseline strictly dominates the board's planar [[288,8,12]] (same n, k and check weight, d 20 against 12); it carries no layout, so it does not enter the 2D-local cells and [[288,8,12]] keeps its local cell.",
  "origin": "baseline"
 },
 "family": "bivariate-bicycle"
}