{
  "id": "2407.19815",
  "version": "v1",
  "published": "2024-07-29T09:06:29.000Z",
  "updated": "2024-07-29T09:06:29.000Z",
  "title": "Weight Enumerators of codes over $\\mathbb{F}_2$ and over $\\mathbb{Z}_4$",
  "authors": [
    "A. K. M. Selim Reza",
    "Manabu Oura",
    "Nur Hamid"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "The symmetrized weight enumerators of pairs of Type II code over $\\mathbb{F}_{2}$ and $\\mathbb{Z}_{4}$, which are invariants for a specified group, have been examined in this paper. It is shown that, for degrees 8 and 16, the space of the invariants ring of that group coincides with the ring generated from those weight enumerators.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-29T09:06:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "symmetrized weight enumerators",
      "invariants",
      "group coincides",
      "specified group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}