A new method to compute sequence correlations over finite fields

Abstract

In this paper we obtain a new method to compute the correlation values of two arbitrary sequences defined by a mapping from 𝔽_4ⁿ to 𝔽₄. We apply this method to demonstrate that the usual nonbinary maximal length sequences have almost ideal correlation under the canonical complex correlation definition and investigate some decimations giving good cross correlation. The techniques we develop are of independent interest for future investigation of sequence design and related problems, including Boolean functions.