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Research Article | Open Access

Arithmetic autocorrelation and pattern distribution of binary sequences

Xi Liu, Huaning Liu( )
Research Center for Number Theory and its Applications, School of Mathematics, Northwest University, Xi'an 710127, China
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Abstract

We clarify a relation between the arithmetic autocorrelation and pattern distribution of binary sequences, then we apply the relation to study the upper bound of arithmetic autocorrelation for two binary sequences constructed by Fermat quotient and the generalized cyclotomic class of order 2, respectively. Our results indicate that the sequences with large "long term" correlations may have small "short term" pattern distribution; and thus have rather small arithmetic autocorrelations.

Keywords

arithmetic autocorrelationFermat quotientgeneralized cyclotomicbinary sequencecharacter sum

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Electronic Research Archive
Volume 33 Issue 2,
February 2025
Pages 849-866
DOI: 10.3934/era.2025038

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Cite this article:
Liu X, Liu H. Arithmetic autocorrelation and pattern distribution of binary sequences. Electronic Research Archive, 2025, 33(2): 849-866. https://doi.org/10.3934/era.2025038

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Received: 03 December 2024
Revised: 24 January 2025
Accepted: 06 February 2025
Published: 15 February 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)