Article
On Irregularities of Distribution of Binary Sequences Relative to Arithmetic Progressions, I. (General Results)
Authors
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Abstract
In 1964 K. F. Roth initiated the study of irregularities of dis- tribution 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 subse- quences 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.
Keywords
arithmetic progressions, well-distribution, binary sequence.
Citation
Dartyge, C., Gyarmati, K., & Sarkozy, A. (2017). On irregularities of distribution of binary sequences relative to arithmetic progressions, i. (general results). Uniform Distribution Theory, 12(1), 55–67. https://doi.org/10.1515/udt-2017-0004
C. Dartyge, K. Gyarmati and A. Sarkozy, “On irregularities of distribution of binary sequences relative to arithmetic progressions, i. (general results),” Uniform Distribution Theory, vol. 12, no. 1, pp. 55–67, 2017, doi: 10.1515/udt-2017-0004.
Dartyge C, Gyarmati K, Sarkozy A. On irregularities of distribution of binary sequences relative to arithmetic progressions, i. (general results). Uniform Distribution Theory. 2017;12(1):55–67. doi:10.1515/udt-2017-0004.
Dartyge, C., Gyarmati, K. and Sarkozy, A. (2017), ‘On irregularities of distribution of binary sequences relative to arithmetic progressions, i. (general results)’, Uniform Distribution Theory, 12(1), pp. 55–67. Available at: https://doi.org/10.1515/udt-2017-0004.
Dartyge, Cecile, et al. “On Irregularities of Distribution of Binary Sequences Relative to Arithmetic Progressions, I. (General Results).” Uniform Distribution Theory, vol. 12, no. 1, 2017, pp. 55–67. https://doi.org/10.1515/udt-2017-0004.
Dartyge, Cecile, Katalin Gyarmati, and Andras Sarkozy. “On Irregularities of Distribution of Binary Sequences Relative to Arithmetic Progressions, I. (General Results).” Uniform Distribution Theory 12, no. 1 (2017): 55–67. https://doi.org/10.1515/udt-2017-0004.
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Published by: Engineering Journals
