{
  "abstract": "We construct an extremal unimodular lattice of rank 37, resolving the last undetermined optimal minimum in ranks at most 48. The construction begins with the Cayley table of $\\mathbb{Z}/13\\mathbb{Z}$, assigning a vector of norm four to each cell. We prove that the resulting incidence lattice has exactly 26 unimodular completions of minimum four, all isometric. The resulting Cayley lattice $Λ$ has automorphism group $\\mathrm{AGL}(1,13)\\times C_6$ and is $s$-extremal, with shadow minimum $13/4$ and kissing number $35\\,594$. An explicit $4$-frame in $Λ$ yields a Type I self-dual $\\mathbb{Z}/4\\mathbb{Z}$-code of length 37 and minimum Euclidean weight 16, resolving the corresponding open case in coding theory.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.07138",
  "author_total": 1,
  "authors": [
    {
      "name": "Eric Kubischta"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/60qey80sn9xnm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.07138",
  "fulltext_url": null,
  "id": "60qey80sn9xnm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.07138",
  "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",
      "math.CO"
    ],
    [
      "arxiv",
      "math.NT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.07138",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/60qey80sn9xnm.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2611.07138",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.07138"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "An extremal unimodular lattice of rank 37",
  "title_text": "An extremal unimodular lattice of rank 37",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:47Z",
  "url": "https://research.draconitic.com/paper/60qey80sn9xnm",
  "venue": "arXiv",
  "versions": []
}