Canonical representation of quasicyclic codes using Gröbner bases theory

The tools and techniques of Gröbner bases theory have proved useful in characterising quasicyclic codes and analysing their algebraic structure. A canonical generating set can be obtained from the reduced Gröbner basis of an associated module structure. The very particular form of this generating set allows straightforward determination of properties such as dimension, in manner directly analogous to the theory developed for cyclic codes.