%0 Journal Article
%T The correlation measures of finite sequences: limiting distributions and minimum values
%A Kai-Uwe Schmidt
%J Mathematics
%D 2014
%I arXiv
%X Three measures of pseudorandomness of finite binary sequences were introduced by Mauduit and S\'ark\"ozy in 1997 and have been studied extensively since then: the normality measure, the well-distribution measure, and the correlation measure of order r. Our main result is that the correlation measure of order r for random binary sequences converges strongly, and so has a limiting distribution. This solves a problem due to Alon, Kohayakawa, Mauduit, Moreira, and R\"odl. We also show that the best known lower bounds for the minimum values of the correlation measures are simple consequences of a celebrated result due to Welch, concerning the maximum nontrivial scalar products over a set of vectors.
%U http://arxiv.org/abs/1404.0172v2