{
  "abstract": "In this paper we give necessary conditions for 4-class association schemes that are generated by double covers of strongly regular graphs. These conditions are applied to open cases for diameter 4 antipodal distance-regular graphs. Using these conditions we are able to show the nonexistence of four cases in the table of Brouwer, Cohen and Neumeier: $\\{20,18,3,1;1,3,18,20\\}$, $\\{22,21,3,1;1,3,21,22\\}$, $\\{ 54,50,5,1;,1,5,50,54 \\}$, $\\{ 170,162,9,1;,1,9,162,170 \\}$. More generally, we show there is no distance-regular graph with intersection array $\\{k,b_1,b_2,1;1,b_2,b_1,k \\}$ where $b_2 \\neq 1$ and $\\frac{ k b_1 }{4}(1+k+\\frac{ k b_1 }{2b_2})$ is odd. Tables are also given for more general 4-class association schemes generated by double covers of strongly regular graphs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05420",
  "author_total": 2,
  "authors": [
    {
      "name": "Patrick Cesarz"
    },
    {
      "name": "Jason Williford"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7s8y3xas39mab.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05420",
  "fulltext_url": null,
  "id": "7s8y3xas39mab",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05420",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Finite Group Theory Research"
    ]
  ],
  "openalex": "W7220690970",
  "pdf_url": "https://arxiv.org/pdf/2610.05420",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7s8y3xas39mab.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.05420",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05420"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Four class association scheme double covers of strongly regular graphs",
  "title_text": "Four class association scheme double covers of strongly regular graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/7s8y3xas39mab",
  "venue": "arXiv",
  "versions": []
}