{
  "id": "2004.03396",
  "version": "v1",
  "published": "2020-04-06T12:25:22.000Z",
  "updated": "2020-04-06T12:25:22.000Z",
  "title": "Strengthening of the Assmus--Mattson theorem for some dual codes",
  "authors": [
    "Tsuyoshi Miezaki",
    "Hiroyuki Nakasora"
  ],
  "comment": "19 pages. arXiv admin note: text overlap with arXiv:1805.10019",
  "categories": [
    "math.CO",
    "cs.IT",
    "math.GR",
    "math.IT",
    "math.NT"
  ],
  "abstract": "We previously proposed the first nontrivial examples of a code having support t-designs for all weights obtained from the Assmus-Mattson theorem and having support t'-designs for some weights with some t'>t. This suggests the possibility of generalizing the Assmus-Mattson theorem, which is very important in design and coding theory. In the present paper, we generalize this example as a strengthening of the Assmus-Mattson theorem along this direction. As a corollary, we provide a new characterization of the extended Golay code G_24.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-06T12:25:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B05",
      "94B05",
      "20B25"
    ],
    "keywords": [
      "assmus-mattson theorem",
      "dual codes",
      "strengthening",
      "first nontrivial examples",
      "extended golay code"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}