{
  "id": "1804.02129",
  "version": "v1",
  "published": "2018-04-06T04:35:16.000Z",
  "updated": "2018-04-06T04:35:16.000Z",
  "title": "Singly even self-dual codes of length $24k+10$ and minimum weight $4k+2$",
  "authors": [
    "Masaaki Harada"
  ],
  "comment": "16 pages",
  "journal": "Cryptography and Communications (2019) 11:597-608",
  "doi": "10.1007/s12095-018-0303-8",
  "categories": [
    "math.CO",
    "cs.IT",
    "math.IT"
  ],
  "abstract": "Currently, the existence of an extremal singly even self-dual code of length $24k+10$ is unknown for all nonnegative integers $k$. In this note, we study singly even self-dual $[24k+10,12k+5,4k+2]$ codes. We give some restrictions on the possible weight enumerators of singly even self-dual $[24k+10,12k+5,4k+2]$ codes with shadows of minimum weight at least $5$ for $k=2,3,4,5$. We discuss a method for constructing singly even self-dual codes with minimal shadow. As an example, a singly even self-dual $[82,41,14]$ code with minimal shadow is constructed for the first time. In addition, as neighbors of the code, we construct singly even self-dual $[82,41,14]$ codes with weight enumerator for which no singly even self-dual code was previously known to exist.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-06T04:35:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "94B05"
    ],
    "keywords": [
      "self-dual code",
      "minimum weight",
      "weight enumerator",
      "minimal shadow",
      "first time"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}