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 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.