1. THE CORRELATION MEASURES OF FINITE SEQUENCES: LIMITING DISTRIBUTIONS AND MINIMUM VALUES.
- Author
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SCHMIDT, KAI-UWE
- Subjects
- *
BINARY sequences , *BINARY number system , *STATISTICAL correlation , *MODULES (Algebra) , *SCALAR field theory - Abstract
Three measures of pseudorandomness of finite binary sequences were introduced by Mauduit and Sárközy 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 Rödl. 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. [ABSTRACT FROM AUTHOR]
- Published
- 2017
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