Cyclic codes and minimal strong Gröbner bases over a principal ideal ring

Authors:
G. H. Norton;A. Salagean
Affiliations:
Department of Mathematics, University of Queensland, Brisbane 4072, Australia;Department of Computer Science, Loughborough University, Loughborough LE11 3TU, UK
Venue:
Finite Fields and Their Applications
Year:
2003

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Abstract

We characterise minimal strong Grobner bases of R[x], where R is a commutative principal ideal ring and deduce a structure theorem for cyclic codes of arbitrary length over R. When R is an Artinian chain ring with residue field R@? and gcd(char(R@?),n)=1, we recover a theorem for cyclic codes of length n over R due to Calderbank and Sloane for R=Z/p^kZ.