{
  "id": "1507.02063",
  "version": "v1",
  "published": "2015-07-08T08:27:48.000Z",
  "updated": "2015-07-08T08:27:48.000Z",
  "title": "On the finite geometry of $W(23,16)$",
  "authors": [
    "Assaf Goldberger"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We study the local geometry of the zero pattern of a weighing matrix $W(23,16)$. The geometry consists of $23$ lines and $23$ points where each line contains $7$ points. The incidence rules are that every two lines intersect in an odd number of points, and the dual statement holds as well. We show that more than $50\\%$ of the pairs of lines must intersect at a single point, and construct a regular weighted graph out of this geometry. This might indicate that a weighing matrix $W(23,16)$ does not exist.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-08T08:27:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite geometry",
      "weighing matrix",
      "dual statement holds",
      "regular weighted graph",
      "geometry consists"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}