{
  "id": "1007.2555",
  "version": "v2",
  "published": "2010-07-15T13:31:39.000Z",
  "updated": "2010-11-24T14:43:48.000Z",
  "title": "Classification of generalized Hadamard matrices H(6,3) and quaternary Hermitian self-dual codes of length 18",
  "authors": [
    "Masaaki Harada",
    "Clement Lam",
    "Akihiro Munemasa",
    "Vladimir D. Tonchev"
  ],
  "comment": "17 pages. Minor revision",
  "journal": "Electronic J. Combin. 17 (2010), R171",
  "categories": [
    "math.CO"
  ],
  "abstract": "All generalized Hadamard matrices of order 18 over a group of order 3, H(6,3), are enumerated in two different ways: once, as class regular symmetric (6,3)-nets, or symmetric transversal designs on 54 points and 54 blocks with a group of order 3 acting semi-regularly on points and blocks, and secondly, as collections of full weight vectors in quaternary Hermitian self-dual codes of length 18. The second enumeration is based on the classification of Hermitian self-dual [18,9] codes over GF(4), completed in this paper. It is shown that up to monomial equivalence, there are 85 generalized Hadamard matrices H(6,3), and 245 inequivalent Hermitian self-dual codes of length 18 over GF(4).",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-11-24T14:43:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B20",
      "94B05"
    ],
    "keywords": [
      "quaternary hermitian self-dual codes",
      "generalized hadamard matrices",
      "classification",
      "inequivalent hermitian self-dual codes",
      "class regular symmetric"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1007.2555H"
    }
  }
}