{
  "id": "2007.01684",
  "version": "v1",
  "published": "2020-07-03T13:50:31.000Z",
  "updated": "2020-07-03T13:50:31.000Z",
  "title": "New Classes of Quantum Codes Associated with Surface Maps",
  "authors": [
    "Debashis Bhowmik",
    "Dipendu Maity",
    "Bhanu Pratap Yadav",
    "Ashish Kumar Upadhyay"
  ],
  "categories": [
    "math.CO",
    "cs.IT",
    "math.IT"
  ],
  "abstract": "If the cyclic sequences of {face types} {at} all vertices in a map are the same, then the map is said to be a semi-equivelar map. In particular, a semi-equivelar map is equivelar if the faces are the same type. Homological quantum codes represent a subclass of topological quantum codes. In this article, we introduce {thirteen} new classes of quantum codes. These codes are associated with the following: (i) equivelar maps of type $ [k^k]$, (ii) equivelar maps on the double torus along with the covering of the maps, and (iii) semi-equivelar maps on the surface of \\Echar{-1}, along with {their} covering maps. The encoding rate of the class of codes associated with the maps in (i) is such that $ \\frac{k}{n}\\rightarrow 1 $ as $ n\\rightarrow\\infty $, and for the remaining classes of codes, the encoding rate is $ \\frac{k}{n}\\rightarrow \\alpha $ as $ n\\rightarrow \\infty $ with $ \\alpha< 1 $.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-03T13:50:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "94Bxx"
    ],
    "keywords": [
      "surface maps",
      "semi-equivelar map",
      "equivelar maps",
      "encoding rate",
      "homological quantum codes represent"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}