Algebraic structure of quasicyclic codes

We use Gröbner bases of modules as a tool in the construction and classification of quasicyclic codes. Whereas previous studies have been mainly concerned with the 1-generator case, our results elucidate the structure of arbitrary quasicyclic codes and their duals. As an application we provide a complete characterisation of self-dual quasicyclic codes of index 2.