Codes and Rings

In this course we survey two types of interaction between codes and rings. First, rings being used as alphabets. The most general class there is quasi Frobenius rings.

Next, rings acting on codes and thereby providing symmetry. Cyclic codes, Quasi-cyclic codes, constacyclic codes. quasi-twisted codes, additive codes will be studied in turn.

The emphasis will be on structural results with some excursion into asymptotics. Thus, we will prove that dihedral codes, double circulant codes, and additive cyclic codes are asymptotically good.