{
  "id": "math/0311046",
  "version": "v1",
  "published": "2003-11-04T20:20:57.000Z",
  "updated": "2003-11-04T20:20:57.000Z",
  "title": "Codes and Invariant Theory",
  "authors": [
    "Gabriele Nebe",
    "E. M. Rains",
    "N. J. A. Sloane"
  ],
  "categories": [
    "math.NT",
    "cs.IT",
    "math.IT"
  ],
  "abstract": "The main theorem in this paper is a far-reaching generalization of Gleason's theorem on the weight enumerators of codes which applies to arbitrary-genus weight enumerators of self-dual codes defined over a large class of finite rings and modules. The proof of the theorem uses a categorical approach, and will be the subject of a forthcoming book. However, the theorem can be stated and applied without using category theory, and we illustrate it here by applying it to generalized doubly-even codes over fields of characteristic 2, doubly-even codes over the integers modulo a power of 2, and self-dual codes over the noncommutative ring $\\F_q + \\F_q u$, where $u^2 = 0$..",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-11-04T20:20:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "94B05",
      "13A50",
      "94B60"
    ],
    "keywords": [
      "invariant theory",
      "arbitrary-genus weight enumerators",
      "generalized doubly-even codes",
      "category theory",
      "gleasons theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....11046N"
    }
  }
}