{
  "id": "2105.09656",
  "version": "v1",
  "published": "2021-05-20T10:40:48.000Z",
  "updated": "2021-05-20T10:40:48.000Z",
  "title": "New hemisystems of the Hermitian surface",
  "authors": [
    "Vincenzo Pallozzi Lavorante",
    "Valentino Smaldore"
  ],
  "categories": [
    "math.CO",
    "math.AG"
  ],
  "abstract": "Finding Hemisystems is a challenging problem and just few examples arising from the Hermitian surface are known. A recent method to obtain Hemisystems is based on using maximal curves. Along this side of research, we provide new examples of Hemisystems in $PG(3,p^2)$, for each prime of the form $p=1+4a^2$, with $ a $ integer. Last, we use these results to obtain two weight linear codes and strongly regular graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-05-20T10:40:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B25",
      "05E30",
      "51E20"
    ],
    "keywords": [
      "hermitian surface",
      "hemisystems",
      "weight linear codes",
      "maximal curves",
      "strongly regular graphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}