{
  "abstract": "We prove a fixed-characteristic density form of the Berger-Charpin conjecture for non-degenerate irreducible cyclic codes: for each prime $p$, the lengths admitting such a non-standard code over some finite field of characteristic $p$ have natural density zero. Thus, for almost every length coprime to $p$, every such code over every finite field of characteristic $p$ has only the permutation automorphisms generated by the cyclic shift and the Frobenius map. The proof uses the Feng--Hollmann--Li--Xiang classification for non-standard irreducible cyclic codes, a normal form for the deriving constructions in that paper, and a theorem by Wiertelak on multiplicative orders, in the form recalled by Moree.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00925",
  "author_total": 4,
  "authors": [
    {
      "name": "Tao Feng"
    },
    {
      "name": "Henk D. L. Hollmann"
    },
    {
      "name": "Weicong Li"
    },
    {
      "name": "Qing Xiang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/31pmcrvvp3jxv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00925",
  "fulltext_url": null,
  "id": "31pmcrvvp3jxv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00925",
  "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.CO"
    ],
    [
      "arxiv",
      "math.IT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00925",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/31pmcrvvp3jxv.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.00925",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00925"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A density theorem for non-standard irreducible cyclic codes",
  "title_text": "A density theorem for non-standard irreducible cyclic codes",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/31pmcrvvp3jxv",
  "venue": "arXiv",
  "versions": []
}