{
  "abstract": "We study two explicit constructions of binary Calderbank--Shor--Steane quantum low-density parity-check (QLDPC) codes with check weight six. The first uses a fixed circulant shift pattern and yields parameters $\\code{6N}{2N+2}{6}$ with Tanner graph girth twelve for $N=31$ and every $N\\ge37$. A graph incidence interpretation gives the ranks and girths, and a uniform weight six logical operator establishes the exact distance. The second construction uses fixed matrix polynomials with circulant and affine permutation coefficients. Here, a polynomial commutation identity guarantees orthogonality for every cyclic lift. Four realizations give $[[192,16,8]]$, $[[288,16,12]]$, $[[384,16,14]]$, and $[[576,32,20]]$, with Tanner girth eight and computationally certified distances. We give reproducible construction data, distinguish classical cycle distance from quantum distance, and identify the limitations of both families.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19451",
  "author_total": 3,
  "authors": [
    {
      "name": "Vahid Nourozi"
    },
    {
      "name": "Roxana Smarandache"
    },
    {
      "name": "David G. M. Mitchell†"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b4fvd3npzgmn6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19451",
  "fulltext_url": null,
  "id": "b4fvd3npzgmn6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19451",
  "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",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "arxiv",
      "math.QA"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7222060456",
  "pdf_url": "https://arxiv.org/pdf/2610.19451",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b4fvd3npzgmn6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.19451",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19451"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "High-Girth QLDPC Codes from Circulant and Affine Permutation Matrices",
  "title_text": "High-Girth QLDPC Codes from Circulant and Affine Permutation Matrices",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/b4fvd3npzgmn6",
  "venue": "arXiv",
  "versions": []
}