{
  "id": "1912.07541",
  "version": "v1",
  "published": "2019-12-16T17:46:54.000Z",
  "updated": "2019-12-16T17:46:54.000Z",
  "title": "Computational Results on the Existence of Primitive Complete Normal Basis Generators",
  "authors": [
    "Dirk Hachenberger",
    "Stefan Hackenberg"
  ],
  "comment": "17 pages",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "We present computational results which strongly support a conjecture of Morgan and Mullen (1996), which states that for every extension $E/F$ of Galois fields there exists a primitive element of $E$ which is completely normal over $F$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-16T17:46:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11T30",
      "12E20"
    ],
    "keywords": [
      "primitive complete normal basis generators",
      "computational results",
      "galois fields",
      "conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}