{
  "id": "1406.1281",
  "version": "v1",
  "published": "2014-06-05T07:16:06.000Z",
  "updated": "2014-06-05T07:16:06.000Z",
  "title": "On codes over R_{k,m} and constructions for new binary self-dual codes",
  "authors": [
    "Nesibe Tufekci",
    "Bahattin Yildiz"
  ],
  "comment": "17 pages",
  "categories": [
    "cs.IT",
    "math.IT"
  ],
  "abstract": "In this work, we study codes over the ring R_{k,m}=F_2[u,v]/<u^{k},v^{m},uv-vu>, which is a family of Frobenius, characteristic 2 extensions of the binary field. We introduce a distance and duality preserving Gray map from R_{k,m} to F_2^{km} together with a Lee weight. After proving the MacWilliams identities for codes over R_{k,m} for all the relevant weight enumerators, we construct many binary self-dual codes as the Gray images of self-dual codes over R_{k,m}. In addition to many extremal binary self-dual codes obtained in this way, including a new construction for the extended binary Golay code, we find 175 new Type I binary self-dual codes of parameters [72,36,12] and 105 new Type II binary self-dual codes of parameter [72,36,12].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-06-05T07:16:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "94B05",
      "94B99"
    ],
    "keywords": [
      "construction",
      "extremal binary self-dual codes",
      "duality preserving gray map",
      "relevant weight enumerators",
      "extended binary golay code"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1406.1281T"
    }
  }
}