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Measures of pseudorandomness of binary lattices, III ( $Q_k$, correlation, normality, minimal values)

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Author(s): Katalin Gyarmati | Christian Mauduit | András Sárközy

Journal: Uniform Distribution Theory
ISSN 1336-913X

Volume: 5;
Issue: 2;
Start page: 183;
Date: 2010;
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Keywords: Binary lattice | pseudorandom | correlation | normality

ABSTRACT
In an earlier paper Hubert, Mauduit and Sárközy defined the notion of binary lattice, they introduced the measures of pseudorandomness of binary lattices, and they constructed a binary lattice with strong pseudorandom properties with respect to these measures. Later further constructions of this type have been given by different authors. In this series we study the measures of pseudorandomness of binary lattices. In particular, in this paper first we study the minimum of the measure $Q_k$ in one dimension. Then we introduce the correlation measure $C_k$ in $n$ dimensions, and we estimate the minima of $Q_k$, $C_k$ and the normality measures in two dimensions. The connection between the correlation measures of order two and three of binary lattices is also studied.

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