{
  "id": "2310.14281",
  "version": "v1",
  "published": "2023-10-22T12:22:21.000Z",
  "updated": "2023-10-22T12:22:21.000Z",
  "title": "$t$-designs obtained from two shells and exceptional examples of them",
  "authors": [
    "Madoka Awada"
  ],
  "comment": "15 pages. arXiv admin note: text overlap with arXiv:2309.03206; text overlap with arXiv:2305.03285 by other authors",
  "categories": [
    "math.CO",
    "cs.IT",
    "math.GR",
    "math.IT",
    "math.NT"
  ],
  "abstract": "In this paper, we construct $3$-designs using extended quadratic residue codes over $\\mathbb {F}_q$ and their dual codes. We give as a corollary $3$-designs that do not follow from the transitivity argument and the Assmus--Mattson Theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-22T12:22:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "94B05",
      "05B05"
    ],
    "keywords": [
      "exceptional examples",
      "extended quadratic residue codes",
      "dual codes",
      "transitivity argument",
      "assmus-mattson theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}