{
  "id": "1509.09158",
  "version": "v1",
  "published": "2015-09-30T12:44:09.000Z",
  "updated": "2015-09-30T12:44:09.000Z",
  "title": "Necessary conditions for the existence of 3-designs over finite fields with nontrivial automorphism groups",
  "authors": [
    "Maarten De Boeck",
    "Anamari Nakic"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "A q-design with parameters t-(v,k,lambda_t)_q is a pair (V, B) of the v-dimensional vector space V over GF(q) and a collection B of k-dimensional subspaces of V, such that each t-dimensional subspace of V is contained in precisely lambda_t members of B. In this paper we give new general necessary conditions on the existence of designs over finite fields with parameters 3-(v, k , lambda_3)_q with a prescribed automorphism group. These necessary conditions are based on a tactical decomposition of such a design over a finite field and are given in the form of equations for the coefficients of tactical decomposition matrices. In particular, they represent necessary conditions on the existence of q-analogues of Steiner systems admitting a prescribed automorphism group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-30T12:44:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B05"
    ],
    "keywords": [
      "finite field",
      "nontrivial automorphism groups",
      "prescribed automorphism group",
      "general necessary conditions",
      "v-dimensional vector space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150909158D"
    }
  }
}