{
  "id": "1509.06913",
  "version": "v1",
  "published": "2015-09-23T10:24:22.000Z",
  "updated": "2015-09-23T10:24:22.000Z",
  "title": "A coloring of the square of the 8-cube with 13 colors",
  "authors": [
    "Janne I. Kokkala",
    "Patric R. J. Östergård"
  ],
  "comment": "3 pages",
  "categories": [
    "math.CO",
    "cs.IT",
    "math.IT"
  ],
  "abstract": "Let $\\chi_{\\bar{k}}(n)$ be the number of colors required to color the $n$-dimensional hypercube such that no two vertices with the same color are at a distance at most $k$. In other words, $\\chi_{\\bar{k}}(n)$ is the minimum number of binary codes with minimum distance at least $k+1$ required to partition the $n$-dimensional Hamming space. By giving an explicit coloring, it is shown that $\\chi_{\\bar{2}}(8)=13$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-23T10:24:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "minimum number",
      "dimensional hypercube",
      "dimensional hamming space",
      "minimum distance"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 3,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150906913K"
    }
  }
}