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- W2016083683 abstract "We present a unified theory of Gröbner 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’ Gröbner basis for the code. We give some applications to cyclic codes." @default.
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- W2016083683 date "2001-04-01" @default.
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- W2016083683 title "Strong Gröbner bases and cyclic codes over a finite-chain ring." @default.
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- W2016083683 doi "https://doi.org/10.1016/s1571-0653(04)00175-1" @default.
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