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arXiv · 1509.06913

A coloring of the square of the 8-cube with 13 colors

Janne I. Kokkala·Patric R. J. Östergård
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Abstract

Let $χ_{\bar{k}}(n)$ 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, $χ_{\bar{k}}(n)$ 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 $χ_{\bar{2}}(8)=13$.

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Janne I. Kokkala, Patric R. J. Östergård. 2015-09-23. A coloring of the square of the 8-cube with 13 colors. https://arxiv.org/abs/1509.06913

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