{
  "id": "2007.01609",
  "version": "v1",
  "published": "2020-07-03T10:59:50.000Z",
  "updated": "2020-07-03T10:59:50.000Z",
  "title": "A family of linear maximum rank distance codes consisting of square matrices of any even order",
  "authors": [
    "Giovanni Longobardi",
    "Corrado Zanella"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "A class of scattered linearized polynomials covering infinitely many field extensions is exhibited. More precisely, the $q$-polynomial over $\\mathbb F_{q^6}$, $q \\equiv 1\\pmod 4$ described in arXiv:1906.05611, arXiv:1910.02278 is generalized for any even $n\\ge6$ to an $\\mathbb F_q$-linear automorphism of $\\mathbb F_q^n$ of order $n$ and proved to be scattered along with some of its iterated compositions. In particular this provides new maximum scattered linear sets of the projective line $\\mathrm{PG}(1,q^n)$ for $n=8,10$. The polynomials described in this paper yield to a new infinite family of MRD-codes in $\\mathbb F_q^{n\\times n}$ with minimum distance $n-1$ for any odd $q$ if $n\\equiv0\\pmod4$ and any $q\\equiv1\\pmod4$ if $n\\equiv2\\pmod4$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-03T10:59:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "51E20",
      "05B25",
      "51E22"
    ],
    "keywords": [
      "linear maximum rank distance codes",
      "maximum rank distance codes consisting",
      "square matrices",
      "polynomial"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}