{
  "id": "1609.03755",
  "version": "v1",
  "published": "2016-09-13T10:35:17.000Z",
  "updated": "2016-09-13T10:35:17.000Z",
  "title": "Perfect codes in Cayley graphs",
  "authors": [
    "He Huang",
    "Binzhou Xia",
    "Sanming Zhou"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We study perfect codes and related objects such as total perfect codes and perfect $t$-codes in Cayley graphs from the viewpoint of group rings. We give a uniform approach to such objects that enables us to obtain new results as well as generalizations of a few known results. In particular, we obtain conditions for a normal subgroup of a finite group to be a perfect code in some Cayley graph of the group. We also discuss related group-theoretic aspects of this approach and pose three open problems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-13T10:35:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cayley graph",
      "study perfect codes",
      "total perfect codes",
      "normal subgroup",
      "finite group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}