A general approach to construction and determination of the linear complexity of sequences based on cosets

Abstract

We give a general approach to $N$-periodic sequences over a finite field $\F_q$ constructed via a subgroup $D$ of the group of invertible elements modulo $N$. Well known examples are Legendre sequences or the two-prime generator. For some generalizations of sequences considered in the literature and for some new examples of sequence constructions we determine the linear complexity.