{
  "id": "2208.09077",
  "version": "v1",
  "published": "2022-08-18T21:54:00.000Z",
  "updated": "2022-08-18T21:54:00.000Z",
  "title": "A note on the Assmus--Mattson theorem for some binary codes II",
  "authors": [
    "Eiichi Bannai",
    "Tsuyoshi Miezaki",
    "Hiroyuki Nakasora"
  ],
  "comment": "15 pages. arXiv admin note: text overlap with arXiv:2208.08617",
  "categories": [
    "math.CO",
    "cs.IT",
    "math.GR",
    "math.IT",
    "math.NT"
  ],
  "abstract": "Let $C$ be a four-weight code, which has all one vector. Furthermore, we assume that $C_\\ell$ are $t$-designs for all $\\ell$ by the Assmus--Mattson theorem. We previously showed that $t\\leq 5$. In the present paper, we show an analogue of this result in the cases of five and six-weight codes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-18T21:54:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B05",
      "94B05",
      "20B25"
    ],
    "keywords": [
      "assmus-mattson theorem",
      "binary codes",
      "four-weight code",
      "six-weight codes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}