{
  "id": "1904.04242",
  "version": "v1",
  "published": "2019-04-07T13:10:13.000Z",
  "updated": "2019-04-07T13:10:13.000Z",
  "title": "Infinite families of $2$-designs from a class of cyclic codes with two non-zeros",
  "authors": [
    "Xiaoni Du",
    "Rong Wang",
    "Cuiling Fan"
  ],
  "comment": "arXiv admin note: substantial text overlap with arXiv:1903.07459",
  "categories": [
    "math.CO"
  ],
  "abstract": "Combinatorial $t$-designs have wide applications in coding theory, cryptography, communications and statistics. It is well known that the supports of all codewords with a fixed weight in a code may give a $t$-design. In this paper, we first determine the weight distribution of a class of linear codes derived from the dual of extended cyclic code with two non-zeros. We then obtain infinite families of $2$-designs and explicitly compute their parameters from the supports of all the codewords with a fixed weight in the codes. By simple counting argument, we obtain exponentially many $2$-designs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-07T13:10:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "infinite families",
      "fixed weight",
      "first determine",
      "wide applications",
      "weight distribution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}