Finite quasi-Frobenius modules, applications to codes and linear recurrences

A simple exposition of the main properties of the quasi-Frobenius modules over finite commutative rings with identity elements. The presented results show the special role of such modules in the theory of linear recurrences and in the theory of linear codes over rings and modules. In particular it is proved that the general weight functions of the linear code over a ring and the dual code over the corresponding $QF$-module are connected by the Mac-Williams identity.