{
  "id": "1401.6254",
  "version": "v2",
  "published": "2014-01-24T03:54:09.000Z",
  "updated": "2014-03-19T08:46:02.000Z",
  "title": "On a 5-design related to a putative extremal doubly even self-dual code of length a multiple of 24",
  "authors": [
    "Masaaki Harada"
  ],
  "comment": "16 pages, Designs, Codes and Cryptogr. (to appear)",
  "categories": [
    "math.CO",
    "cs.IT",
    "math.IT"
  ],
  "abstract": "By the Assmus and Mattson theorem, the codewords of each nontrivial weight in an extremal doubly even self-dual code of length 24m form a self-orthogonal 5-design. In this paper, we study the codes constructed from self-orthogonal 5-designs with the same parameters as the above 5-designs. We give some parameters of a self-orthogonal 5-design whose existence is equivalent to that of an extremal doubly even self-dual code of length 24m for m=3,...,6. If $m \\in \\{1,\\ldots,6\\}$, $k \\in \\{m+1,\\ldots,5m-1\\}$ and $(m,k) \\ne (6,18)$, then it is shown that an extremal doubly even self-dual code of length 24m is generated by codewords of weight 4k.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-03-19T08:46:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "94B05",
      "05B30"
    ],
    "keywords": [
      "self-dual code",
      "putative extremal doubly",
      "self-orthogonal",
      "length 24m form",
      "nontrivial weight"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.6254H"
    }
  }
}