On lower bounds to the maximum correlation of complex roots-of-unity sequences

Abstract

It is shown how the Welch bound (1974) on the maximum correlation of families of complex sequences of fixed norm can be modified to provide an improved bound for the case when the sequence symbols are roots of unity. As in the Welch bound, the improved bound is based on a useful expression for the even correlation moments. An analysis of the ratio of successive even moments using this expression is shown to yield a small improvement over a similarly derived bound due to V.M. Sidelnikov (1971). Interestingly, the expression for the moments reduces in the binary (q=2) case to a version of the Pless power-moment identities. The derivation also provides insight into the problem of optimal sequence design.