{
  "id": "0707.2173",
  "version": "v4",
  "published": "2007-07-14T21:26:13.000Z",
  "updated": "2009-03-30T04:47:15.000Z",
  "title": "Cyclic (v;r,s;lambda) difference families with two base blocks and v <= 50",
  "authors": [
    "Dragomir Z. Djokovic"
  ],
  "comment": "39 pages, 6 tables. Minor corrections, a new SDS inserted. Abridged version to appear in Annals of Combinatorics",
  "categories": [
    "math.CO"
  ],
  "abstract": "We construct many new cyclic (v;r,s;lambda) difference families with v less than or equal 50. In particular we construct the difference families with parameters (45;18,10;9), (45;22,22;21), (47;21,12;12), (47;19,15;12), (47;22,14;14), (48;20,10;10), (48;24,4;12), (50;25,20;20) for which the existence question was an open problem. The (45;22,22;21) difference family gives a BIBD with parameters v=45, b=90, r=44, k=22 and lambda=21, and the one with parameters (50;25,20;20) gives a pair of binary sequences of length 50 with zero periodic autocorrelation function (the periodic analog of a Golay pair). We also construct nine new D-optimal designs. A normal form for cyclic difference families is proposed and used effectively in compiling the list of known and new difference families.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2009-03-30T04:47:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B20",
      "05B30"
    ],
    "keywords": [
      "difference family",
      "base blocks",
      "zero periodic autocorrelation function",
      "parameters",
      "cyclic difference families"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0707.2173D"
    }
  }
}