On finite pseudorandom binary sequences VII: The measures of pseudorandomness

Abstract

In an earlier paper the authors introduced the well-distribution measure and correlation measure of order k as the measures of pseudorandomness of finite pseudorandom binary sequences. In this paper first these measures are studied for a truly random sequence selected from f1;+1g . Next the minimum of these measures over all sequences EN 2 f1;+1g is estimated. Finally, the connection between correlations of different orders is studied.