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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 perfect/quasi-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.