{
  "abstract": "Additive codes over $\\Ffour$ that are self-orthogonal under the trace inner product correspond to binary quantum stabilizer codes. We study 1-generator $(1,2)$-quasi-cyclic (QC) additive codes and their exact quantum distances. For composite lengths $n=\\ell m$, an ancestor-lifting theorem transports dual words of the folded ancestor to the length-$n$ code. A two-layer decomposition for $\\ell=2$ and a CRT splitting for odd $\\ell$ yield dimension laws and explain equality, escape, and mixed-branch behavior in the certified examples. A palindromic criterion ensures symplectic self-orthogonality, while reversal pairing and a symplectic Gram rank formula describe broader construction families. Exact distances are established by information-set decoding screening, Brouwer--Zimmermann computation on the additive dual, and independent witness verification. We certify twenty-one record-breaking binary quantum codes across twenty entries of Grassl's code table, with twenty-eight certified members in total. Propagation improves thirty-four further entries, and explicit constructions are supplied for three table-tying GV entries marked Code Missing Construction. Six additional candidates are reported only with rigorous upper bounds and heuristic screening evidence. The results connect divisor-lattice structure in additive quasi-cyclic codes with reproducible certification of exact quantum distances.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.36700",
  "author_total": 4,
  "authors": [
    {
      "name": "Liangdong Lu"
    },
    {
      "name": "Ran Xu"
    },
    {
      "name": "Ruipan Yang"
    },
    {
      "name": "Qiang Fu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1fxd9n4t5jc5y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.36700",
  "fulltext_url": null,
  "id": "1fxd9n4t5jc5y",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.36700",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Coding theory and cryptography"
    ]
  ],
  "openalex": "W7224128131",
  "pdf_url": "https://arxiv.org/pdf/2610.36700",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1fxd9n4t5jc5y.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:50Z",
      "native_id": "2610.36700",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.36700"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Ancestor Lifting of Quasi-Cyclic Additive Codes and Certified Quantum Codes",
  "title_text": "Ancestor Lifting of Quasi-Cyclic Additive Codes and Certified Quantum Codes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/1fxd9n4t5jc5y",
  "venue": "arXiv",
  "versions": []
}