{
  "id": "1707.02003",
  "version": "v1",
  "published": "2017-07-07T00:36:14.000Z",
  "updated": "2017-07-07T00:36:14.000Z",
  "title": "Infinite families of 2-designs from GA_1(q) actions",
  "authors": [
    "Hao Liu",
    "Cunsheng Ding"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Group action is a standard approach to obtain $t$-designs. In this approach, selecting a specific permutation group with a certain degree of transitivity or homogeneity and a proper set of base blocks is important for obtaining $t$-$(v, k, \\lambda)$ designs with computable parameters $t, v, k$, and $\\lambda$. The general affine group $\\GA_1(q)$ is $2$-transitive on $\\gf(q)$, and has relatively a small size. In this paper, we determine the parameters of a number of infinite families of $2$-designs obtained from the action of the group $\\GA_1(q)$ on certain base blocks, and demonstrate that some of the $2$-designs give rise to linear codes with optimal or best parameters known. Open problems are also presented.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-07T00:36:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B05",
      "51E10",
      "94B15"
    ],
    "keywords": [
      "infinite families",
      "base blocks",
      "specific permutation group",
      "general affine group",
      "best parameters"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}