{
  "id": "1706.03218",
  "version": "v1",
  "published": "2017-06-10T10:53:39.000Z",
  "updated": "2017-06-10T10:53:39.000Z",
  "title": "Extremal Type II $\\mathbb{Z}_4$-codes constructed from binary doubly even self-dual codes of length $40$",
  "authors": [
    "Masaaki Harada"
  ],
  "comment": "6 pages",
  "categories": [
    "math.CO",
    "cs.IT",
    "math.IT"
  ],
  "abstract": "In this note, we demonstrate that every binary doubly even self-dual code of length $40$ can be realized as the residue code of some extremal Type II $\\mathbb{Z}_4$-code. As a consequence, it is shown that there are at least $94356$ inequivalent extremal Type II $\\mathbb{Z}_4$-codes of length $40$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-10T10:53:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "94B05"
    ],
    "keywords": [
      "self-dual code",
      "binary doubly",
      "inequivalent extremal type",
      "residue code"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}