Technical Report CS0077

Title: Some Optimization Problems for Convolution Systems over Finite Groups
Authors: M.G. Karpovsky and E.A. Trachtenberg
Abstract: We define and study many-dimensional linear invariant discrete systems over finite groups. We consider the problem of optimum synthesis of such systems computing a given input/output pair. The optimum solution (or estimates for them) are obtained on the basis of two very simply computed criteria. Conditions are studied for the existence of an idempotent impulse function of a linear system over a group, computing a given input/output pair. The best approximation Is found for many-dimensional linear invariant systems, defined on a finite interval of discrete time by systems over the given finite group.
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