{
  "id": "1709.00926",
  "version": "v1",
  "published": "2017-09-04T12:47:29.000Z",
  "updated": "2017-09-04T12:47:29.000Z",
  "title": "New maximum scattered linear sets of the projective line",
  "authors": [
    "Bence Csajbók",
    "Giuseppe Marino",
    "Ferdinando Zullo"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "In [2] and [19] are presented the first two families of maximum scattered $\\mathbb{F}_q$-linear sets of the projective line $\\mathrm{PG}(1,q^n)$. More recently in [23] and in [5], new examples of maximum scattered $\\mathbb{F}_q$-subspaces of $V(2,q^n)$ have been constructed, but the equivalence problem of the corresponding linear sets is left open. Here we show that the $\\mathbb{F}_q$-linear sets presented in [23] and in [5], for $n=6,8$, are new. Also, for $q$ odd, $q\\equiv \\pm 1,\\,0 \\pmod 5$, we present new examples of maximum scattered $\\mathbb{F}_q$-linear sets in $\\mathrm{PG}(1,q^6)$, arising from trinomial polynomials, which define new $\\mathbb{F}_q$-linear MRD-codes of $\\mathbb{F}_q^{6\\times 6}$ with dimension $12$, minimum distance 5 and middle nucleus (or left idealiser) isomorphic to $\\mathbb{F}_{q^6}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-04T12:47:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "51E20",
      "51E22",
      "05B25"
    ],
    "keywords": [
      "maximum scattered linear sets",
      "projective line",
      "left idealiser",
      "middle nucleus",
      "minimum distance"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}