Abstract
Abstract: In studying the scalability of optical networks, one problem arising involves coloring the vertices of the n-dimensional hypercube with as few colors as possible such that any two vertices whose Hamming distance is at most k are colored differently. Determining the exact value of \chi_{\bar k}(n), the minimum number of colors needed, appears to be a difficult problem. In this paper, we improve the known lower and upper bounds of \chi_{\bar k}(n) and indicate the connection of this coloring problem to linear codes.