Measures of Pseudorandomness: Arithmetic Autocorrelation and Correlation Measure

Richard Hofer (), László Mérai () and Arne Winterhof ()
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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

A chapter in Number Theory – Diophantine Problems, Uniform Distribution and Applications, 2017, pp 303-312 from Springer

Abstract: 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.

Keywords: Binary Sequence; Linear Complexity; Correlation Measure; Primitive Element; Positive Degree (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-55357-3_15

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DOI: 10.1007/978-3-319-55357-3_15

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