{
  "id": "1601.00443",
  "version": "v1",
  "published": "2016-01-04T10:36:24.000Z",
  "updated": "2016-01-04T10:36:24.000Z",
  "title": "On the dual code of points and generators on the Hermitian variety $\\mathcal{H}(2n+1,q^2)$",
  "authors": [
    "Maarten De Boeck",
    "Peter Vandendriessche"
  ],
  "journal": "Adv. Math. Commun. 8 (2014), no. 3, 281-296",
  "doi": "10.3934/amc.2014.8.281",
  "categories": [
    "math.CO"
  ],
  "abstract": "We study the dual linear code of points and generators on a non-singular Hermitian variety $\\mathcal{H}(2n+1,q^2)$. We improve the earlier results for $n=2$, we solve the minimum distance problem for general $n$, we classify the $n$ smallest types of code words and we characterize the small weight code words as being a linear combination of these $n$ types.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-04T10:36:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "51E20",
      "51E22",
      "05B25",
      "94B05"
    ],
    "keywords": [
      "dual code",
      "generators",
      "small weight code words",
      "non-singular hermitian variety",
      "minimum distance problem"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160100443D"
    }
  }
}