A Coloring Of The Square Of The 8-cube With 13 Colors

Kokkala Janne I., Östergård Patric R. J.. Arxiv 2015

[Paper]    
ARXIV

Let ${\chi }_{\overline{k}}(n)$ 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, ${\chi }_{\overline{k}}(n)$ 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 ${\chi }_{\overline{2}}(8)=13$.

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