{
  "id": "1505.04611",
  "version": "v1",
  "published": "2015-05-18T12:39:40.000Z",
  "updated": "2015-05-18T12:39:40.000Z",
  "title": "A Generalization of Combinatorial Designs Related to Almost Difference Sets",
  "authors": [
    "Jerod Michel",
    "Baokun Ding"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper we study a certain generalization of combinatorial designs related to almost difference sets, namely the $t$-adesign, which was coined by Cunsheng Ding in 2015. It is clear that $2$-adesigns are a kind of partially balanced incomplete block design which naturally arise in many combinatorial and statistical problems. We discuss some of their basic properties and give several constructions of $2$-adesigns (some of which correspond to new almost difference sets, and others of which correspond to new almost difference families), as well as two constructions of $3$-adesigns. We also discuss some basic properties of their incidence matrices and codes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-18T12:39:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "combinatorial designs",
      "difference sets",
      "generalization",
      "basic properties",
      "partially balanced incomplete block design"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150504611M"
    }
  }
}