{
  "id": "1403.6012",
  "version": "v2",
  "published": "2014-03-24T15:47:58.000Z",
  "updated": "2014-06-01T03:08:11.000Z",
  "title": "New results on permutation polynomials over finite fields",
  "authors": [
    "Xiaoer Qin",
    "Guoyou Qian",
    "Shaofang Hong"
  ],
  "comment": "11 pages. To appear in International Journal of Number Theory",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper, we get several new results on permutation polynomials over finite fields. First, by using the linear translator, we construct permutation polynomials of the forms $L(x)+\\sum_{j=1}^k \\gamma_jh_j(f_j(x))$ and $x+\\sum_{j=1}^k\\gamma_jf_j(x)$. These generalize the results obtained by Kyureghyan in 2011. Consequently, we characterize permutation polynomials of the form $L(x)+\\sum_{i=1} ^l\\gamma_i {\\rm Tr}_{{\\bf F}_{q^m}/{\\bf F}_{q}}(h_i(x))$, which extends a theorem of Charpin and Kyureghyan obtained in 2009.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-06-01T03:08:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite fields",
      "construct permutation polynomials",
      "kyureghyan",
      "characterize permutation polynomials",
      "linear translator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1403.6012Q"
    }
  }
}