{
  "id": "1911.09526",
  "version": "v1",
  "published": "2019-11-19T19:59:27.000Z",
  "updated": "2019-11-19T19:59:27.000Z",
  "title": "A family of permutation trinomials in $\\mathbb{F}_{q^2}$",
  "authors": [
    "Daniele Bartoli",
    "Marco Timpanella"
  ],
  "categories": [
    "math.CO",
    "math.AG"
  ],
  "abstract": "Let $p>3$ and consider a prime power $q=p^h$. We completely characterize permutation polynomials of $\\mathbb{F}_{q^2}$ of the type $f_{a,b}(X) = X(1 + aX^{q(q-1)} + bX^{2(q-1)}) \\in \\mathbb{F}_{q^2}[X]$. In particular, using connections with algebraic curves over finite fields, we show that the already known sufficient conditions are also necessary.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-11-19T19:59:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "permutation trinomials",
      "prime power",
      "characterize permutation polynomials",
      "algebraic curves",
      "finite fields"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}