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Measures of Pseudorandomness: Arithmetic Autocorrelation and Correlation Measure

In: Number Theory – Diophantine Problems, Uniform Distribution and Applications

Author

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  • Richard Hofer

    (Austrian Academy of Sciences, Johann Radon Institute for Computational and Applied Mathematics)

  • László Mérai

    (Austrian Academy of Sciences, Johann Radon Institute for Computational and Applied Mathematics)

  • Arne Winterhof

    (Austrian Academy of Sciences, Johann Radon Institute for Computational and Applied Mathematics)

Abstract

We prove a relation between two measures of pseudorandomness, the arithmetic autocorrelation, and the correlation measure of order k. Roughly speaking, we show that any binary sequence with small correlation measure of order k up to a sufficiently large k cannot have a large arithmetic correlation. We apply our result to several classes of sequences including Legendre sequences defined with polynomials.

Suggested Citation

  • Richard Hofer & László Mérai & Arne Winterhof, 2017. "Measures of Pseudorandomness: Arithmetic Autocorrelation and Correlation Measure," Springer Books, in: Christian Elsholtz & Peter Grabner (ed.), Number Theory – Diophantine Problems, Uniform Distribution and Applications, pages 303-312, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-55357-3_15
    DOI: 10.1007/978-3-319-55357-3_15
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