{
  "id": "1208.2942",
  "version": "v1",
  "published": "2012-08-14T18:58:08.000Z",
  "updated": "2012-08-14T18:58:08.000Z",
  "title": "A New Approach to Permutation Polynomials over Finite Fields, II",
  "authors": [
    "Neranga Fernando",
    "Xiang-dong Hou",
    "Stephen D. Lappano"
  ],
  "comment": "47 pages, 3 tables",
  "categories": [
    "math.CO",
    "math.NT"
  ],
  "abstract": "Let $p$ be a prime and $q$ a power of $p$. For $n\\ge 0$, let $g_{n,q}\\in\\Bbb F_p[{\\tt x}]$ be the polynomial defined by the functional equation $\\sum_{a\\in\\Bbb F_q}({\\tt x}+a)^n=g_{n,q}({\\tt x}^q-{\\tt x})$. When is $g_{n,q}$ a permutation polynomial (PP) of $\\Bbb F_{q^e}$? This turns out to be a challenging question with remarkable breath and depth, as shown in the predecessor of the present paper. We call a triple of positive integers $(n,e;q)$ {\\em desirable} if $g_{n,q}$ is a PP of $\\Bbb F_{q^e}$. In the present paper, we find many new classes of desirable triples whose corresponding PPs were previously unknown. Several new techniques are introduced for proving a given polynomial is a PP.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-08-14T18:58:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11T06",
      "11T55"
    ],
    "keywords": [
      "permutation polynomial",
      "finite fields",
      "functional equation",
      "techniques",
      "predecessor"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 47,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1208.2942F"
    }
  }
}