New bounds on a hypercube coloring problem

In studying the scalability of optical networks, one problem which arises involves coloring the vertices of the n-cube 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((k) over bar)(n), the minimum number of colors needed, appears to be a difficult problem. In this note, we improve the known lower and upper bounds of chi((k) over bar)(n) and indicate the connection of this coloring problem to linear codes. (C) 2002 Elsevier Science B.V. All rights reserved.