{
  "id": "1510.05736",
  "version": "v1",
  "published": "2015-10-20T02:04:53.000Z",
  "updated": "2015-10-20T02:04:53.000Z",
  "title": "Cretan(4t+1) Matrices",
  "authors": [
    "N. A. Balonin",
    "Jennifer Seberry"
  ],
  "comment": "16 pages, 7 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "A $Cretan(4t+1)$ matrix, of order $4t+1$, is an orthogonal matrix whose elements have moduli $\\leq 1$. The only $Cretan(4t+1)$ matrices previously published are for orders 5, 9, 13, 17 and 37. This paper gives infinitely many new $Cretan(4t+1)$ matrices constructed using $regular~Hadamard$ matrices, $SBIBD(4t+1,k,\\lambda)$, weighing matrices, generalized Hadamard matrices and the Kronecker product. We introduce an inequality for the radius and give a construction for a Cretan matrix for every order $n \\geq 3$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-20T02:04:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B20",
      "G.2.1"
    ],
    "keywords": [
      "kronecker product",
      "orthogonal matrix",
      "cretan matrix",
      "generalized hadamard matrices"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151005736B"
    }
  }
}