%0 Journal Article
%T A coloring of the square of the 8-cube with 13 colors
%A Janne I. Kokkala
%A Patric R. J. £¿sterg£¿rd
%J Mathematics
%D 2015
%I arXiv
%X 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 $\chi_{\bar{2}}(8)=13$.
%U http://arxiv.org/abs/1509.06913v1