Constructions of pseudorandom binary lattices using cyclotomic classes in finite fields

Abstract

In 2006, Hubert, Mauduit and Sárközy extended the notion of binary sequences to n-dimensional binary lattices and introduced the measures of pseudorandomness of binary lattices. In 2011, Gyarmati, Mauduit and Sárközy extended the notions of family complexity, collision and avalanche effect from binary sequences to binary lattices. In this paper, we construct pseudorandom binary lattices by using cyclotomic classes in finite fields and study the pseudorandom measure of order k, family complexity, collision and avalanche effect. Results indicate that such binary lattices are “good,” and their families possess a nice structure in terms of family complexity, collision and avalanche effect.