{
  "id": "1302.3281",
  "version": "v2",
  "published": "2013-02-14T00:49:32.000Z",
  "updated": "2016-03-01T04:20:19.000Z",
  "title": "Constructing commutative semifields of square order",
  "authors": [
    "Stephen M. Gagola III",
    "Joanne L. Hall"
  ],
  "categories": [
    "math.CO",
    "math.AC",
    "quant-ph"
  ],
  "abstract": "The projection construction has been used to construct semifields of odd characteristic using a field and a twisted semifield [Commutative semifields from projection mappings, Designs, Codes and Cryptography, 61 (2011), 187--196]. We generalize this idea to a projection construction using two twisted semifields to construct semifields of odd characteristic. Planar functions and semifields have a strong connection so this also constructs new planar functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-02-14T00:49:32.000Z",
      "title": "Two families of planar functions on F_{p^{2r}}",
      "abstract": "Two new families of planar functions are constructed. These new families are part of a more general construction which also includes a family of planar functions recently constructed by Bierbrauer [Commutative semifields from projection mappings, Designs, Codes and Cryptography, 61 (2011), 187--196].",
      "comment": "22 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2016-03-01T04:20:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "51E15",
      "05B25",
      "51A40",
      "94A60"
    ],
    "keywords": [
      "planar functions",
      "general construction",
      "projection mappings",
      "commutative semifields"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1302.3281G"
    }
  }
}