Large families of pseudorandom binary lattices by using the multiplicative inverse modulo P

Abstract

Hubert, Mauduit and Sárközy introduced pseudorandom measures for finite pseudorandom binary lattices. Gyarmati, Mauduit, Sárközy and Stewart presented some natural and flexible constructions, which are the two-dimensional extensions and modifications of a few one-dimensional constructions. The upper estimates for the pseudorandom measures of their binary lattices are based on the principle that character sums or exponential sums in two variables can be estimated by fixing one of the variables. In this paper, we constructed two large families of [Formula: see text] dimensional pseudorandom binary lattices by using the multiplicative inverse modulo [Formula: see text], and study the properties: pseudorandom measure, collision and avalanche effect.