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Algorithms and structures for convolutions over Galois fields

The computation of cyclic convolutions in Galois fields is an integral part of coding theory and formulation as well as of many signal processing applications. In this paper, we introduce a method for the computation of such convolutions that minimizes, in theory, the computational complexity of the algorithm. We also propose special-purpose computer architecture schemes for the efficient realization of the algorithm, and in general, for efficient calculation of convolutions in Galois fields.