Large families of pseudo-random subsets formed by generalized cyclotomic classes

Abstract

Recently, Dartyge and Sarkozy defined the measures, i.e., the well- distribution measure and the correlation measure of order k, of pseudo-randomness of subsets of the set {1, 2, . . . , N}, and they presented several examples for subsets with strong pseudo-random properties when N is a prime number. In this article, we present a construction of pseudo-random subsets for N = pq and give some partial results on the pseudo-random measures.