{
  "id": "1506.00392",
  "version": "v1",
  "published": "2015-06-01T08:44:54.000Z",
  "updated": "2015-06-01T08:44:54.000Z",
  "title": "Further results on multiple coverings of the farthest-off points",
  "authors": [
    "Daniele Bartoli",
    "Alexander A. Davydov",
    "Massimo Giulietti",
    "Stefano Marcugini",
    "Fernanda Pambianco"
  ],
  "comment": "30 pages, 3 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "Multiple coverings of the farthest-off points ($(R,\\mu)$-MCF codes) and the corresponding $(\\rho,\\mu)$-saturating sets in projective spaces $PG(N,q)$ are considered. We propose and develop some methods which allow us to obtain new small $(1,\\mu)$-saturating sets and short $(2,\\mu)$-MCF codes with $\\mu$-density either equal to 1 (optimal saturating sets and almost perfect MCF-codes) or close to 1 (roughly $1+1/cq$, $c\\ge1$). In particular, we provide new algebraic constructions and some bounds. Also, we classify minimal and optimal $(1,\\mu)$-saturating sets in $PG(2,q)$, $q$ small.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-01T08:44:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "multiple coverings",
      "farthest-off points",
      "mcf codes",
      "algebraic constructions",
      "perfect mcf-codes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150600392B"
    }
  }
}