{
  "abstract": "The generalized covering radii have recently emerged as fundamental parameters of linear codes with applications to database linear querying. In this paper, we study the generalized covering radii $ρ_t(M(m,q))$ of Melas codes $M(m,q)$ over any finite field $\\mathbb{F}_q$. We determine $ρ_2(M(m,q))$ for all $q$, and for a general $t \\ge 3$, we prove that $ρ_t(M(m,q)) \\in \\left\\{2t,2t+1\\right\\}$ for $q \\in \\{2,3\\}$ and $ρ_t(M(m,q))=2t$ for $q \\ge 4$ whenever $m$ is sufficiently large. These results extend recent work on the covering radius of Melas codes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.29906",
  "author_total": 2,
  "authors": [
    {
      "name": "Shuxing Li"
    },
    {
      "name": "Maosheng Xiong"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bpmdnvznmhr7m.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.29906",
  "fulltext_url": null,
  "id": "bpmdnvznmhr7m",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.29906",
  "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": "W7204919917",
  "pdf_url": "https://arxiv.org/pdf/2608.29906",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bpmdnvznmhr7m.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2608.29906",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.29906"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "The generalized covering radii of Melas codes",
  "title_text": "The generalized covering radii of Melas codes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/bpmdnvznmhr7m",
  "venue": "arXiv",
  "versions": []
}