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/sub k//sup 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. Further, 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.

Lee distance Gray codes for k-ary n-cubes and torus networks are presented. Using these Lee distance Gray codes, it is further shown how to directly generate edge disjoint Hamiltonian cycles for a class of k-ary n-cubes, 2-D tori, and hypercubes.

This paper investigates methods to locate system resources, such as expensive hardware or software modules, to provide the most effective cost/performance trade-offs in a torus parallel machine. This paper contains some solutions to perfect distance-t and perfectiquasi-perfect j-adjacency placement in a k-ary n-cube and a torus using Lee distance error-correcting codes. It also presents generalized resource placement (j-adjacency with distance-t placement) methods based on the concept of covering radius of Lee distance codes.