{
  "id": "2309.08081",
  "version": "v1",
  "published": "2023-09-15T00:51:42.000Z",
  "updated": "2023-09-15T00:51:42.000Z",
  "title": "A note on the Assmus--Mattson theorem for some non-binary codes (a resume)",
  "authors": [
    "Eiichi Bannai",
    "Tsuyoshi Miezaki",
    "Hiroyuki Nakasora"
  ],
  "comment": "6 pages, this is a resume of \"A note on the Assmus--Mattson theorem for some non-binary codes\"",
  "categories": [
    "math.CO",
    "cs.IT",
    "math.IT"
  ],
  "abstract": "Let $C$ be a two and three-weight ternary code. Furthermore, we assume that $C_\\ell$ are $t$-designs for all $\\ell$ by the Assmus--Mattson theorem. We show that $t \\leq 5$. As a corollary, we provide a new characterization of the (extended) ternary Golay code.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-15T00:51:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B05",
      "94B05",
      "20B25"
    ],
    "keywords": [
      "assmus-mattson theorem",
      "non-binary codes",
      "ternary golay code",
      "three-weight ternary code",
      "characterization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}