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New bounds on a hypercube coloring problem and linear codes

By Hung Quang Ngo, Ding-zhu Du and Ronald L. Graham


In studying the scalability of optical networks, one problem arising involves coloring the vertices of the ¡-dimensional hypercube with as few colors as possible such that any two vertices whose Hamming distance is at ¢ most are colored differently. Determining the exact value of ¡� © , the minimum number of colors needed, appears to be a difficult problem. In this paper, we improve the known lower and upper bounds of £� ¤ § ¡� © and indicate the connec-tion of this coloring problem to linear codes

Topics: hypercube, coloring, linear codes
Year: 2001
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