{
  "abstract": "In this paper, we establish a tight upper bound for the size of a $(v,5,3,1)$ optical orthogonal code (OOC) and call such a code optimal when it achieves this upper bound. In addition, if an optimal OOC has the property that all non-identity elements of $\\mathbb{Z}_v$ are covered by the list of differences of its codeword-sets then it is called perfect. In this paper, we present direct and recursive constructions for infinite classes of optimal and perfect $(v,5,3,1)$-OOCs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.30003",
  "author_total": 4,
  "authors": [
    {
      "name": "Laura Johnson"
    },
    {
      "name": "Lorenzo Mella"
    },
    {
      "name": "Anita Pasotti"
    },
    {
      "name": "Emma Smith"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5gjm447k60ec3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30003",
  "fulltext_url": null,
  "id": "5gjm447k60ec3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.30003",
  "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",
      "2208|graph theory and CDMA systems"
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  "openalex": "W7223247316",
  "pdf_url": "https://arxiv.org/pdf/2610.30003",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5gjm447k60ec3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.30003",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30003"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "On optimal (v,5,3,1) optical orthogonal codes",
  "title_text": "On optimal (v,5,3,1) optical orthogonal codes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/5gjm447k60ec3",
  "venue": "arXiv",
  "versions": []
}