## Linear recurring sequences over rings and modules

Here we present some fundamental concept and results of the theory of linear recurring sequences over rings and modules and their applications. Of course, the authors give in more detail those results that are close to their mathematical interests. In particular, an attempt has been made to construct a general algebraic theory of k-LRS over modules, paying explicit attention to periodic k-sequences, to properties of linear recurrences over finite rings and especially over Galois rings, and also to methods of constructing codes baed on such recurrences.