%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