{
  "abstract": "Let $\\text{RM}(r,n)$ be the $r$th order Reed-Mullet code of length $2^n$, and let $ρ(r,n)$ denote its covering radius. It is known that $242\\leρ(1,9)\\le 244$, and the determination of $ρ(1,9)$ is a long-standing open question. We give a computer-assisted proof that $ρ(1,9)=242$, leveraging the classification of the $349$ orbits in $\\text{RM}(3,9)/\\text{RM}(2,9)$ under $\\text{GL}(9,2)$ [1,3]. The notebook to verify the computer search portion, Verify_RM(1,9).ipynb, contains all data and recomputes each check, and may be found in the repository https://github.com/FreemanSlaughter/Covering-Radius.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00070",
  "author_total": 3,
  "authors": [
    {
      "name": "Xiang-Dong Hou"
    },
    {
      "name": "Evelyn Sabo"
    },
    {
      "name": "Freeman Slaughter"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9w0qtxxttan4e.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00070",
  "fulltext_url": null,
  "id": "9w0qtxxttan4e",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00070",
  "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.CO"
    ],
    [
      "arxiv",
      "math.IT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00070",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9w0qtxxttan4e.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.00070",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00070"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "The covering radius of RM(1,9) is precisely 242",
  "title_text": "The covering radius of RM(1,9) is precisely 242",
  "type": "preprint",
  "updated_at": "2026-11-04T15:21:05Z",
  "url": "https://research.draconitic.com/paper/9w0qtxxttan4e",
  "venue": "arXiv",
  "versions": []
}