{
  "abstract": "We construct quantum codes from codewords of a cyclic code and the minors of a polynomial matrix. The construction uses a two-row, three-column matrix whose minors yield a second matrix satisfying the CSS orthogonality condition. We derive the code dimension from the greatest common divisors of the entries and minors, with a simplified formula for odd lifting factors. A residue characterization identifies additional common factors of the minors and leads to a method for controlling the dimension through polynomial selection. We also give a condition for changing the minor generator without changing the code. Explicit polynomial constructions yield 13 quantum codes with verified minimum distances, including a $[[255,80,12]]$ code of rate $80/255$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19459",
  "author_total": 3,
  "authors": [
    {
      "name": "Vahid Nourozi"
    },
    {
      "name": "Roxana Smarandache"
    },
    {
      "name": "David G. M. Mitchell"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dhwje30n5a0mf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19459",
  "fulltext_url": null,
  "id": "dhwje30n5a0mf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19459",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.QA"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Coding theory and cryptography"
    ]
  ],
  "openalex": "W7221914407",
  "pdf_url": "https://arxiv.org/pdf/2610.19459",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dhwje30n5a0mf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:31Z",
      "native_id": "2610.19459",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19459"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Quantum LDPC Codes from Polynomial Minors",
  "title_text": "Quantum LDPC Codes from Polynomial Minors",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/dhwje30n5a0mf",
  "venue": "arXiv",
  "versions": []
}