{
  "id": "0902.1901",
  "version": "v2",
  "published": "2009-02-11T14:42:52.000Z",
  "updated": "2011-08-14T09:26:02.000Z",
  "title": "Optimal Curves of Genus 3 over Finite Fields with Discriminant -19",
  "authors": [
    "E. Alekseenko",
    "S. Aleshnikov",
    "N. Markin",
    "A. Zaytsev"
  ],
  "comment": "table of curves was corrected",
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "In this work we study the properties of maximal and minimal curves of genus 3 over finite fields with discriminant -19. We prove that any such curve can be given by an explicit equation of certain form. Using these equations we obtain a table of maximal and minimal curves over finite fields with discriminant -19 of cardinality up to 997. We also show that existence of a maximal curve implies that there is no minimal curve and vice versa.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-08-14T09:26:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite fields",
      "optimal curves",
      "discriminant",
      "minimal curve",
      "maximal curve implies"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0902.1901A"
    }
  }
}