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 "distance": {
  "d": 12,
  "P": {
   "value": 12,
   "confidence": "upper_bound",
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 "provenance": {
  "authors": [
   "@cbjuan"
  ],
  "construction": "Perturbed bivariate bicycle (PBB) code: ell=12, m=6 cyclic group ring F2[x,y]/(x^12-1,y^6-1); A=x+x^2y, B=1+xy^5+x^11y^4, C-perturbation=xy^3+x^10y^3, D-perturbation=xy^5+x^10y^5 (0-indexed exponent pairs: A=[[1,2],[10,3],[10,4]], B=[[0,0],[1,5],[11,4]], C=[[1,3],[10,3]], D=[[1,5],[10,5]]); stabilizer matrix H=(A B | C D; 0 0 | B^T A^T) per the paper's PBB convention",
  "origin": "submission",
  "date": "2026-10-07",
  "model": "Claude Opus 4.6, GPT-5.3-Codex, Gemini 3.1 Pro",
  "references": [
   "arXiv:2606.02418"
  ],
  "notes": "First published in arXiv:2606.02418 (the non-CSS PBB catalog, Campaign 5 therein; code_id 12_6_0193, bliss_hash 2176a91d34df3783). Checked for duplication against the current board: no existing stabilizer-board entry at this [[n,k,d]]. Shares the slug with a pre-existing CSS baseline entry (codes/144-12-12.json, Bravyi et al. arXiv:2308.07915) by coincidence of parameters only -- this is a genuinely different, non-CSS construction (ranked on the separate stabilizer board per TRACKS.md), filed as the -b variant per CONTRIBUTING.md's slug-sharing convention."
 },
 "family": "bivariate-bicycle"
}