{
  "aliases": null,
  "backlinks": null,
  "body": "\n## Summary\n\nIn graph theory, the **Berlekamp–Van Lint–Seidel graph** is a locally linear strongly regular graph with parameters $(243,22,1,2)$. This means that it has 243 vertices, 22 edges per vertex (for a total of 2673 edges), exactly one shared neighbor per pair of adjacent vertices, and exactly two shared neighbors per pair of non-adjacent vertices. It was constructed by Elwyn Berlekamp, J. H. van Lint, and Johan Jacob Seidel as the coset graph of the ternary Golay code.\n",
  "commit": "68a8c3dc73fd55004b2796431c607c30960d1a85",
  "front": {
    "inventory": [
      "PDYKVS3DR2"
    ],
    "kind": "concept",
    "name": "Berlekamp–Van Lint–Seidel graph",
    "same_as": {
      "wikidata": "Q61743750",
      "wikipedia": "Berlekamp–Van Lint–Seidel graph"
    },
    "sources": [
      {
        "locator": "Berlekamp–Van Lint–Seidel graph",
        "mention": "wikipedia://en/59945606",
        "note": "adopted",
        "sections": [
          "Summary"
        ],
        "wikipedia": "en:59945606@r1360618382"
      }
    ],
    "tag": "ATVXY7XAKE"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/ATVXY7XAKE/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/ATVXY7XAKE.md",
  "msc": null,
  "name": "Berlekamp–Van Lint–Seidel graph",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/ATV/ATVXY7XAKE.md",
  "status": null,
  "tag": "ATVXY7XAKE",
  "uri": "m2://ATVXY7XAKE",
  "url": "https://math2.tamnd.com/wiki/berlekamp-van-lint-seidel-graph/",
  "writing": {
    "tag": "ATVXY7XAKE",
    "kind": "concept",
    "level": "W1",
    "next": [
      {
        "what": "edge defines in",
        "note": "at least one definition",
        "have": 0,
        "want": 1
      },
      {
        "what": "edge instance_of in",
        "note": "at least two examples",
        "have": 0,
        "want": 2
      },
      {
        "what": "edge not_instance_of in",
        "note": "at least one non-example",
        "have": 0,
        "want": 1
      },
      {
        "what": "edge specializes both",
        "note": "the more general notions and the special cases",
        "have": 0,
        "want": 1
      }
    ]
  }
}
