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A method for constructing a logic circuit for inversion in finite field GF(2.sup.m) is described, where m=nk, and k, n are coprime numbers, using bases in subfields GF(2.sup.n) and GF(2.sup.k). The method may be applied to error correction codes, including BCH codes, Reed-Solomon codes (which are a subset of BCH codes), turbo codes, and the like.