{
  "id": "2306.03391",
  "version": "v1",
  "published": "2023-06-06T04:11:55.000Z",
  "updated": "2023-06-06T04:11:55.000Z",
  "title": "New results on linear permutation polynomials with coefficients in a subfield",
  "authors": [
    "Elías Javier García Claro",
    "Gustavo Terra Bastos"
  ],
  "categories": [
    "math.RT",
    "math.GR",
    "math.RA"
  ],
  "abstract": "Some families of linear permutation polynomials of $\\mathbb{F}_{q^{ms}}$ with coefficients in $\\mathbb{F}_{q^{m}}$ are explicitly described (via conditions on their coefficients) as isomorphic images of classical subgroups of the general linear group of degree $m$ over the ring $\\frac{\\mathbb{F}_{q}[x]}{\\left\\langle x^{s}-1 \\right\\rangle}$. In addition, the sizes of some of these families are computed. Finally, several criteria to construct linear permutation polynomials of $\\mathbb{F}_{q^{2p}}$ (where $p$ is a prime number) with prescribed coefficients in $\\mathbb{F}_{q^{2}}$ are given. Examples illustrating the main results are presented.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-06-06T04:11:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "coefficients",
      "construct linear permutation polynomials",
      "general linear group",
      "isomorphic images",
      "main results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}