On correlations of a family of generalized geometric sequences

In this paper we study families of generalized geometric sequences formed by applying a feedforward function to certain sums of decimated m-sequences with elements in a finite field. We compute their correlation functions, which for certain families turn out to be close to the square root of the period. The size of these families equals their period. We also show that in the binary case the linear complexities of these sequences are much larger than those of cascaded geometric sequences, although in these cases the maximum correlations are larger.