<abstract xmlns="http://www.w3.org/1999/xhtml"><p> In 1964 K. F. Roth initiated the study of irregularities of distribution of binary sequences relative to arithmetic progressions and since that numerous papers have been written on this subject. In the applications one needs binary sequences which are well distributed relative to arithmetic progressions, in particular, in cryptography one needs binary sequences whose short subsequences are also well-distributed relative to arithmetic progressions. Thus we introduce weighted measures of pseudorandomness of binary sequences to study this property. We study the typical and minimal values of this measure for binary sequences of a given length.</p></abstract>

In 1964 K. F. Roth initiated the study of irregularities of distribution of binary sequences relative to arithmetic progressions and since that numerous papers have been written on this subject. In the applications one needs binary sequences which are well distributed relative to arithmetic progressions, in particular, in cryptography one needs binary sequences whose short subsequences are also well-distributed relative to arithmetic progressions. Thus we introduce weighted measures of pseudorandomness of binary sequences to study this property. We study the typical and minimal values of this measure for binary sequences of a given length.

On Irregularities of Distribution of Binary Sequences Relative to Arithmetic Progressions, I. (General Results)

Uniform distribution theory

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

In 1964 K. F. Roth initiated the study of irregularities of distribution of binary sequences relative to arithmetic progressions and since that numerous papers...

On Irregularities of Distribution of Binary Sequences Relative to Arithmetic Progressions, I. (General Results)

Article Category: Dedicated to the fifth international conference on Uniform Distribution Theory (UDT 2016) Sopron, Hungary, July 5–8, 2016

Published Online: Jul 22, 2017

Page range: 55 - 67

Received: Oct 22, 2015

Accepted: Jan 23, 2016

DOI: https://doi.org/10.1515/udt-2017-0004

Keywords
arithmetic progressions, well-distribution, binary sequence

© 2017

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

On Irregularities of Distribution of Binary Sequences Relative to Arithmetic Progressions, I. (General Results)

Article Category: Dedicated to the fifth international conference on Uniform Distribution Theory (UDT 2016) Sopron, Hungary, July 5–8, 2016

Published Online: Jul 22, 2017

Page range: 55 - 67

Received: Oct 22, 2015

Accepted: Jan 23, 2016

DOI: https://doi.org/10.1515/udt-2017-0004

Keywordsarithmetic progressions, well-distribution, binary sequence

© 2017

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

Keywords
arithmetic progressions, well-distribution, binary sequence