On the Partial-Period Correlation Moments of GMW Sequences

Recently, Scholtz and Welch showed how Gordon-Mills-Welch (GMW) difference sets could be made to yield sequences which in addition to sharing identical full-period correlation properties with m-sequences also have large linear span. In this paper, we examine the partial-period (p-p) correlation properties of GMW sequences and provide closed-form expressions for their even p-p correlation moments. An upper bound is derived for the fourth order p-p correlation moment of a large class of GMW sequences and is shown to be close to a lower bound derived from the general p-p correlation moment expression for arbitrary binary sequences given earlier by Kumar. These bounds are tabulated for several specific GMW sequences.