{
  "id": "1709.05536",
  "version": "v1",
  "published": "2017-09-16T16:13:25.000Z",
  "updated": "2017-09-16T16:13:25.000Z",
  "title": "Construction of full diversity $D_n$-lattices for all $n$",
  "authors": [
    "Robson R. de Araujo",
    "Grasiele C. Jorge"
  ],
  "comment": "16 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper we construct some families of rotated $D_n$-lattices with full diversity for any $n$. These lattices can be good for signal transmission over both Gaussian and Rayleigh fading channels. In order to get bounds for their minimum product distances, we show that the $Z$-modules used in \\cite{sethoggier} to obtain rotated $\\mathbb{Z}^{n}$-lattices with $n$ odd are ideals and find a sufficient condition for such ideals being principal ideals.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-16T16:13:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "full diversity",
      "construction",
      "minimum product distances",
      "sufficient condition",
      "signal transmission"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}