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arXiv · 1608.02354

The cross-correlation measure of families of finite binary sequences: limiting distributions and minimal values

László Mérai
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Abstract

Gyarmati, Mauduit and S\'ark\"ozy introduced the cross-correlation measure $\Phi_k(G)$ of order $k$ to measure the level of pseudorandom properties of families of finite binary sequences. In an earlier paper we estimated the cross-correlation measure of a random family of binary sequences. In this paper, we sharpen these earlier results by showing that for random families, the cross-correlation measure converges strongly, and so has limiting distribution. We also give sharp bounds to the minimum values of the cross-correlation measure, which settles a problem of Gyarmati, Mauduit and S\'ark\"ozy nearly completely.

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László Mérai. 2016-08-08. The cross-correlation measure of families of finite binary sequences: limiting distributions and minimal values. https://arxiv.org/abs/1608.02354

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