Improving results on the pseudorandomness of sequences generated via the additive order of a finite field

Abstract

We improve several results in the area of pseudorandom sequences. First, we obtain an improved bound on the general lattice test for digital explicit inversive and digital explicit nonlinear pseudorandom number generators. Second, we improve the bound on the correlation measure of binary sequences generated by the quadratic character of finite fields. Finally, we improve the bound on the correlation measure of digital explicit inversive pseudorandom numbers, and the bound on their linear complexity profile.Although we follow essentially the earlier proofs, we improved a crucial step, namely a better estimate on the number of nonempty intersections of ‘boxes’ of a finite field is given.