Mersenne numbers in the bases of systems of residual classes when transmitting data in serial communication channels
In this paper, we consider the system of residual classes for data representation in communication channels. In this case, it is possible to perform parallel data processing without taking into account digit transfers. However, the most of communication channels are serial; therefore, we also consid...
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2022
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ir-20.500.12258-186152022-05-26T10:00:14Z Mersenne numbers in the bases of systems of residual classes when transmitting data in serial communication channels Smirnov, A. A. Смирнов, А. А. Bondar, V. V. Бондарь, В. В. Rozhenko, O. D. Роженко, О. Д. Mirzoyan, M. V. Мирзоян, М. В. Darzhaniya, A. D. Даржания, А. Д. System of residual classes Amount of information Fermat number Mersenne number Parallel communication channel In this paper, we consider the system of residual classes for data representation in communication channels. In this case, it is possible to perform parallel data processing without taking into account digit transfers. However, the most of communication channels are serial; therefore, we also consider the possibility of serial transmission of parallel data. We show that the use of the system of residual classes of Mersenne numbers as a base does not lead to decreasing the data transmission rate. We estimate the amount of information contained in the positions of the numbers of a positional code. 2022-02-01T07:53:53Z 2022-02-01T07:53:53Z 2022 Статья Smirnov A. A., Bondar V. V., Rozhenko, O. D., Mirzoian, M. V., Darjania A. D. Mersenne numbers in the bases of systems of residual classes when transmitting data in serial communication channels // Journal of Mathematical Sciences (United States). - 2022. - Volume 260. - No. 2. - Pages 241 - 248. - DOI10.1007/s10958-022-05688-0 http://hdl.handle.net/20.500.12258/18615 en Journal of Mathematical Sciences (United States) application/pdf Springer |
| institution |
СКФУ |
| collection |
Репозиторий |
| language |
English |
| topic |
System of residual classes Amount of information Fermat number Mersenne number Parallel communication channel |
| spellingShingle |
System of residual classes Amount of information Fermat number Mersenne number Parallel communication channel Smirnov, A. A. Смирнов, А. А. Bondar, V. V. Бондарь, В. В. Rozhenko, O. D. Роженко, О. Д. Mirzoyan, M. V. Мирзоян, М. В. Darzhaniya, A. D. Даржания, А. Д. Mersenne numbers in the bases of systems of residual classes when transmitting data in serial communication channels |
| description |
In this paper, we consider the system of residual classes for data representation in communication channels. In this case, it is possible to perform parallel data processing without taking into account digit transfers. However, the most of communication channels are serial; therefore, we also consider the possibility of serial transmission of parallel data. We show that the use of the system of residual classes of Mersenne numbers as a base does not lead to decreasing the data transmission rate. We estimate the amount of information contained in the positions of the numbers of a positional code. |
| format |
Статья |
| author |
Smirnov, A. A. Смирнов, А. А. Bondar, V. V. Бондарь, В. В. Rozhenko, O. D. Роженко, О. Д. Mirzoyan, M. V. Мирзоян, М. В. Darzhaniya, A. D. Даржания, А. Д. |
| author_facet |
Smirnov, A. A. Смирнов, А. А. Bondar, V. V. Бондарь, В. В. Rozhenko, O. D. Роженко, О. Д. Mirzoyan, M. V. Мирзоян, М. В. Darzhaniya, A. D. Даржания, А. Д. |
| author_sort |
Smirnov, A. A. |
| title |
Mersenne numbers in the bases of systems of residual classes when transmitting data in serial communication channels |
| title_short |
Mersenne numbers in the bases of systems of residual classes when transmitting data in serial communication channels |
| title_full |
Mersenne numbers in the bases of systems of residual classes when transmitting data in serial communication channels |
| title_fullStr |
Mersenne numbers in the bases of systems of residual classes when transmitting data in serial communication channels |
| title_full_unstemmed |
Mersenne numbers in the bases of systems of residual classes when transmitting data in serial communication channels |
| title_sort |
mersenne numbers in the bases of systems of residual classes when transmitting data in serial communication channels |
| publisher |
Springer |
| publishDate |
2022 |
| url |
https://dspace.ncfu.ru/handle/20.500.12258/18615 |
| work_keys_str_mv |
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