{
  "id": "2109.14962",
  "version": "v1",
  "published": "2021-09-30T09:50:34.000Z",
  "updated": "2021-09-30T09:50:34.000Z",
  "title": "Embedding in MDS codes and Latin cubes",
  "authors": [
    "Vladimir N. Potapov"
  ],
  "comment": "7 pages",
  "journal": "Journal of Combinatorial Designs. 2022. V. 30 (9). P. 626--633",
  "doi": "10.1002/jcd.21849",
  "categories": [
    "math.CO"
  ],
  "abstract": "An embedding of a code is a mapping that preserves distances between codewords. We prove that any code with code distance $\\rho$ and length $d$ can be embedded into an MDS code with the same code distance and length but under a larger alphabet. As a corollary we obtain embeddings of systems of partial mutually orthogonal Latin cubes and $n$-ary quasigroups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-09-30T09:50:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B15"
    ],
    "keywords": [
      "mds code",
      "code distance",
      "partial mutually orthogonal latin cubes",
      "larger alphabet",
      "preserves distances"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}