Mersenne numbers in the bases of systems of residual classes when transmitting data in serial communication channels

Abstract

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.