{
  "id": "2301.03569",
  "version": "v1",
  "published": "2023-01-09T18:41:02.000Z",
  "updated": "2023-01-09T18:41:02.000Z",
  "title": "Codes and modular curves",
  "authors": [
    "Alain Couvreur"
  ],
  "comment": "Lecture notes for a course given at the Algebraic Coding Theory (ACT) summer school 2022",
  "categories": [
    "math.NT",
    "cs.IT",
    "math.AG",
    "math.IT"
  ],
  "abstract": "These lecture notes have been written for a course at the Algebraic Coding Theory (ACT) summer school 2022 that took place in the university of Zurich. The objective of the course propose an in-depth presentation of the proof of one of the most striking results of coding theory: Tsfasman Vl\\u{a}du\\c{t} Zink Theorem, which asserts that for some prime power $q$, there exist sequences of codes over $\\mathbb{F}_q$ whose asymptotic parameters beat random codes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-01-09T18:41:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "modular curves",
      "asymptotic parameters beat random codes",
      "in-depth presentation",
      "zink theorem",
      "prime power"
    ],
    "tags": [
      "lecture notes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}