Geodesic
Mersenne numbers in the bases of systems of residual classes when transmitting data in serial communication channels
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the IV International Scientific Conference "Actual Problems of Applied Mathematics". Kabardino-Balkar Republic, Nalchik, Elbrus Region, May 22–26, 2018. Part II, Tome 166 (2019), pp. 87-94

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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 transfers in bits. However, most of the communication channels are serial; in this regard, the possibility of serial transmission of parallel data is considered. We show that the use of the residual classes of Mersenne numbers as bases of the system does not lead to a decrease in the data transfer rate. The amount of information contained in the positions of the numbers of the positional code is estimated.
Keywords: Mersenne number, Fermat number, system of residual classes, parallel communication channels, amount of information. 
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     author = {A. A. Smirnov and V. V. Bondar and O. D. Rozhenko and M. V. Mirzoyan and A. D. Darjania},
     title = {Mersenne numbers in the bases of systems of residual classes when transmitting data in serial communication channels},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {87--94},
     publisher = {mathdoc},
     volume = {166},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2019_166_a8/}
}
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A. A. Smirnov; V. V. Bondar; O. D. Rozhenko; M. V. Mirzoyan; A. D. Darjania. Mersenne numbers in the bases of systems of residual classes when transmitting data in serial communication channels. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the IV International Scientific Conference "Actual Problems of Applied Mathematics". Kabardino-Balkar Republic, Nalchik, Elbrus Region, May 22–26, 2018. Part II, Tome 166 (2019), pp. 87-94. http://geodesic.mathdoc.fr/item/INTO_2019_166_a8/