Generalized constructions of polyphase sequence families using shift and addition of multiplicative character sequences

In this paper, generalized constructions of polyphase sequence families from the shift and addition of power residue and Sidelnikov sequences are presented. Initially, ψ(0) = 1 is assumed for multiplicative characters ψ to represent power residue and Sidelnikov sequences in a simple form. The Weil bound on multiplicative character sums is refined for the assumption, where the character sums are equivalent to the correlations of sequences represented by multiplicative characters. Generalized constructions are then presented by the addition of multiple cyclic shifts of power residue and Sidelnikov sequences. The refined Weil bound is employed to provide efficient proofs on the maximum correlation magnitudes of the generalized sequence families.