<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In 2009, Grant, Shallit, and Stoll [Acta Arith. <bold>140</bold> (2009), [345–368] constructed a large family of pseudorandom sequences, called generalized Rudin--Shapiro sequences, for which they established some results about the average of discrete correlation coefficients of order 2 in cases where the size of the alphabet is a prime number or a squarefree product of primes. We establish similar results for an even larger family of pseudorandom sequences, constructed via difference matrices, in the case of an alphabet of any size. The constructions generalize those from Grant et al. In the case where the size of the alphabet is squarefree and where there are at least two prime factors, we obtain an improvement in the error term by comparison with the result of Grant et al.</p></abstract>

In 2009, Grant, Shallit, and Stoll [Acta Arith. 140 (2009), [345–368] constructed a large family of pseudorandom sequences, called generalized Rudin--Shapiro sequences, for which they established some results about the average of discrete correlation coefficients of order 2 in cases where the size of the alphabet is a prime number or a squarefree product of primes. We establish similar results for an even larger family of pseudorandom sequences, constructed via difference matrices, in the case of an alphabet of any size. The constructions generalize those from Grant et al. In the case where the size of the alphabet is squarefree and where there are at least two prime factors, we obtain an improvement in the error term by comparison with the result of Grant et al.

Discrete Correlation of Order 2 of Generalized Rudin-Shapiro Sequences on Alphabets of Arbitrary Size

Uniform distribution theory

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

In 2009, Grant, Shallit, and Stoll [Acta Arith. 140 (2009), [345–368] constructed a large family of pseudorandom sequences, called generalized Rudin--Shapiro...

Discrete Correlation of Order 2 of Generalized Rudin-Shapiro Sequences on Alphabets of Arbitrary Size

Published Online: Jul 24, 2020

Page range: 1 - 26

Received: Oct 15, 2019

Accepted: Feb 12, 2020

DOI: https://doi.org/10.2478/udt-2020-0001

Keywords
discrete correlation, Rudin-Shapiro sequence, difference matrix, exponential sums

© 2020 Pierre-Adrien Tahay, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Discrete Correlation of Order 2 of Generalized Rudin-Shapiro Sequences on Alphabets of Arbitrary Size

Published Online: Jul 24, 2020

Page range: 1 - 26

Received: Oct 15, 2019

Accepted: Feb 12, 2020

DOI: https://doi.org/10.2478/udt-2020-0001

Keywordsdiscrete correlation, Rudin-Shapiro sequence, difference matrix, exponential sums

© 2020 Pierre-Adrien Tahay, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
discrete correlation, Rudin-Shapiro sequence, difference matrix, exponential sums