A General Approach to Construction and Determination of the Linear Complexity of Sequences Based on Cosets

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We give a general approach to N-periodic sequences over a finite field $\mathbb F_q$ 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.