{
  "id": "2308.01593",
  "version": "v1",
  "published": "2023-08-03T07:55:02.000Z",
  "updated": "2023-08-03T07:55:02.000Z",
  "title": "New constructions of NMDS self-dual codes",
  "authors": [
    "Dongchun Han",
    "Hanbin Zhang"
  ],
  "comment": "12 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Near maximum distance separable (NMDS) codes are important in finite geometry and coding theory. Self-dual codes are closely related to combinatorics, lattice theory, and have important application in cryptography. In this paper, we construct a class of $q$-ary linear codes and prove that they are either MDS or NMDS which depends on certain zero-sum condition. In the NMDS case, we provide an effective approach to construct NMDS self-dual codes which largely extend known parameters of such codes. In particular, we proved that for square $q$, almost $q/8$ NMDS self-dual $q$-ary codes can be constructed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-03T07:55:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "constructions",
      "construct nmds self-dual codes",
      "ary linear codes",
      "nmds case",
      "finite geometry"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}