{
  "abstract": "We study the maximum length of nontrivial simple-root cyclic maximum distance separable (MDS) codes over ${\\mathbb F}_q$. We prove $n\\le q+1$ if $\\gcd(n,q^2-1)>2$, or if the dimension is even and $\\gcd(n,q^2-1)>1$. The bound also holds for all lengths whose prime factors lie in $\\{2,3,5,7\\}$. We obtain further cases involving primes $\\ell\\ge11$ with $(\\ell-1)/2$ prime, under conditions on the exponents and the characteristic. The proofs combine Fourier supports, locality bounds and field descent with arithmetic restrictions on multiplicative orders and prime-adic valuations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.29810",
  "author_total": 4,
  "authors": [
    {
      "name": "Gaojun Luo"
    },
    {
      "name": "Xiwang Cao"
    },
    {
      "name": "Shitao Li"
    },
    {
      "name": "Yang Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2yp1xqz4pss0w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.29810",
  "fulltext_url": null,
  "id": "2yp1xqz4pss0w",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.29810",
  "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"
    ],
    [
      "openalex",
      "1702|Coding theory and cryptography"
    ]
  ],
  "openalex": "W7223206623",
  "pdf_url": "https://arxiv.org/pdf/2610.29810",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2yp1xqz4pss0w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.29810",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.29810"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "On the maximum length of cyclic MDS codes",
  "title_text": "On the maximum length of cyclic MDS codes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/2yp1xqz4pss0w",
  "venue": "arXiv",
  "versions": []
}