{
  "id": "2004.11998",
  "version": "v1",
  "published": "2020-04-24T21:33:17.000Z",
  "updated": "2020-04-24T21:33:17.000Z",
  "title": "Cyclic Sieving for Cyclic Codes",
  "authors": [
    "Alexander Mason",
    "Victor Reiner",
    "Shruthi Sridhar"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Prompted by a question of Jim Propp, this paper examines the cyclic sieving phenomenon (CSP) in certain cyclic codes. For example, it is shown that, among dual Hamming codes over $F_q$, the generating function for codedwords according to the major index statistic (resp. the inversion statistic) gives rise to a CSP when $q=2$ or $q=3$ (resp. when $q=2$). A byproduct is a curious characterization of the irreducible polynomials in $F_2[x]$ and $F_3[x]$ that are primitive.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-24T21:33:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cyclic codes",
      "major index statistic",
      "cyclic sieving phenomenon",
      "inversion statistic",
      "jim propp"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}