{
  "id": "1507.08503",
  "version": "v1",
  "published": "2015-07-30T13:49:07.000Z",
  "updated": "2015-07-30T13:49:07.000Z",
  "title": "A New Approach to Examine q-Steiner Systems",
  "authors": [
    "Tuvi Etzion"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "The interest in $q$-analogs of codes and designs has been increased in the last few years as a consequence of their new application in error-correction for random network coding. Two of the most intriguing problems are the existence question of an infinite family of $q$-analog of Steiner systems, excepts for spreads, and the existence question for $q$-analog for the Fano plane. We exhibit a new method to attack these problems. In the process we define a new family of designs whose existence is implied from the existence of q-analog of Steiner systems, but their existence can be also independent. We present necessary conditions for the existence for such designs, trivial constructions for such designs, and a nontrivial recursive construction.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-30T13:49:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "q-steiner systems",
      "existence question",
      "nontrivial recursive construction",
      "trivial constructions",
      "necessary conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}