{
  "id": "math/0308046",
  "version": "v1",
  "published": "2003-08-05T22:22:41.000Z",
  "updated": "2003-08-05T22:22:41.000Z",
  "title": "Still better nonlinear codes from modular curves",
  "authors": [
    "Noam D. Elkies"
  ],
  "comment": "10 pages",
  "categories": [
    "math.NT",
    "cs.IT",
    "math.AG",
    "math.IT"
  ],
  "abstract": "We give a new construction of nonlinear error-correcting codes over suitable finite fields k from the geometry of modular curves with many rational points over k, combining two recent improvements on Goppa's construction. The resulting codes are asymptotically the best currently known.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-08-05T22:22:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "94B27",
      "94B65"
    ],
    "keywords": [
      "better nonlinear codes",
      "modular curves",
      "nonlinear error-correcting codes",
      "goppas construction",
      "rational points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......8046E"
    }
  }
}