{
  "id": "1406.5797",
  "version": "v1",
  "published": "2014-06-23T02:32:52.000Z",
  "updated": "2014-06-23T02:32:52.000Z",
  "title": "Constructions of A Large Class of Optimum Constant Weight Codes over F_2",
  "authors": [
    "Masao Kasahara",
    "Shigeichi Hirasawa"
  ],
  "categories": [
    "cs.IT",
    "math.IT"
  ],
  "abstract": "A new method of constructing optimum constant weight codes over F_2 based on a generalized $(u, u+v)$ construction is presented. We present a new method of constructing superimposed code $C_{(s_1,s_2,\\cdots,s_I)}^{(h_1, h_2, \\cdots, h_I)}$ bound. and presented a large class of optimum constant weight codes over F_2 that meet the bound due to Brouwer and Verhoeff, which will be referred to as BV . We present large classes of optimum constant weight codes over F_2 for $k=2$ and $k=3$ for $n \\leqq 128$. We also present optimum constant weight codes over F_2 that meet the BV bound for $k=2,3,4,5$ and 6, for $n \\leqq 128$. The authors would like to present the following conjectures : $C_{I}$: $C_{(s_1)}^{(h_1)}$ presented in this paper yields the optimum constant weight codes for the code-length $n=3h_1$, number of information symbols $k=2$ and minimum distance $d=2h_1$ for any positive integer $h_1$. $C_{II}$: $C_{(s_1)}^{(h_1)}$ yields the optimum constant weight codes at $n=7h_1, k=3$ and $d=4h_1$ for any $h_1$. $C_{III}$: Code $C_{(s_1,s_2,\\cdots,s_I)}^{(h_1, h_2, \\cdots, h_I)}$ yields the optimum constant weight codes of length $n=2^{k+1}-2$, and minimum distance $d=2^{k}$ for any number of information symbols $k\\geq 3$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-06-23T02:32:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "large class",
      "construction",
      "constructing optimum constant weight codes",
      "minimum distance",
      "information symbols"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1406.5797K"
    }
  }
}