Abstract
Abstract We present a unified theory of Grobner bases over a principal ideal ring with a view to applications in Coding Theory, for example to the structure of codes over a finite-chain ring, e.g. a Galois ring. Our theory is effective and yields an extension of Buchberger's algorithm to principal ideal rings. In particular, given a set of generators for a cyclic code over a Galois ring, we can compute a ‘minimal strong’ Grobner basis for the code. We give some applications to cyclic codes.
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