On cyclic codes over Galois rings

Abstract Let R be a Galois ring of characteristic p a , where p is a prime and a is a natural number. In this paper, the generators of cyclic codes of arbitrary length n over R in terms of minimal degree polynomials of certain subsets of codes have been obtained. Moreover, the explicit set of generators so obtained turns out to be a minimal strong Grobner basis. Some results on torsion codes of a cyclic code over R have also been obtained. Using these results, the size of a cyclic code over R has been expressed in terms of the degrees of its generators.

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