Journal
IEEE TRANSACTIONS ON COMPUTERS
Volume 52, Issue 10, Pages 1271-1284Publisher
IEEE COMPUTER SOC
DOI: 10.1109/TC.2003.1234525
Keywords
k-ary n-cubes; hypercube; Lee distance; Lee distance gray codes; binary Gray codes; Hamiltonian cycle
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Solutions for decomposing a higher dimensional torus to edge disjoint lower dimensional tori, in particular, edge disjoint Hamiltonian cycles are obtained based on the coding theory approach. First, Lee distance Gray codes in Z(k)(n) are presented and then it is shown how these codes can directly be used to generate edge disjoint Hamiltonian cycles in k-ary n-cubes. IFurther, some new classes of binary Gray codes are designed from these Lee distance Gray codes and, using these new classes of binary Gray codes, edge disjoint Hamiltonian cycles in hypercubes are generated.
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