{
  "id": "1910.02278",
  "version": "v1",
  "published": "2019-10-05T14:33:36.000Z",
  "updated": "2019-10-05T14:33:36.000Z",
  "title": "A new family of maximum scattered linear sets in $\\mathrm{PG}(1,q^6)$",
  "authors": [
    "Daniele Bartoli",
    "Corrado Zanella",
    "Ferdinando Zullo"
  ],
  "categories": [
    "math.CO",
    "cs.IT",
    "math.IT"
  ],
  "abstract": "We generalize the example of linear set presented by the last two authors in \"Vertex properties of maximum scattered linear sets of $\\mathrm{PG}(1,q^n)$\" (2019) to a more general family, proving that such linear sets are maximum scattered when $q$ is odd and, apart from a special case, they are are new. This solves an open problem posed in \"Vertex properties of maximum scattered linear sets of $\\mathrm{PG}(1,q^n)$\" (2019). As a consequence of Sheekey's results in \"A new family of linear maximum rank distance codes\" (2016), this family yields to new MRD-codes with parameters $(6,6,q;5)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-05T14:33:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "51E20",
      "05B25",
      "51E22"
    ],
    "keywords": [
      "maximum scattered linear sets",
      "linear maximum rank distance codes",
      "vertex properties",
      "special case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}