{
  "id": "2401.06085",
  "version": "v1",
  "published": "2024-01-11T18:02:41.000Z",
  "updated": "2024-01-11T18:02:41.000Z",
  "title": "On the stabilizer of the graph of linear functions over finite fields",
  "authors": [
    "Valentino Smaldore",
    "Corrado Zanella",
    "Ferdinando Zullo"
  ],
  "categories": [
    "math.CO",
    "cs.IT",
    "math.IT"
  ],
  "abstract": "In this paper we will study the action of $\\mathbb{F}_{q^n}^{2 \\times 2}$ on the graph of an $\\mathbb{F}_q$-linear function of $\\mathbb{F}_{q^n}$ into itself. In particular we will see that, under certain combinatorial assumptions, its stabilizer (together with the sum and product of matrices) is a field. We will also see some examples for which this does not happen. Moreover, we will establish a connection between such a stabilizer and the right idealizer of the rank-metric code defined by the linear function and give some structural results in the case in which the polynomials are partially scattered.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-11T18:02:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "linear function",
      "finite fields",
      "stabilizer",
      "structural results",
      "right idealizer"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}