Correction Codes in the System of Residual Classes

The report considers correction codes with mutually non-prime bases (CMNPB). To date, almost no one has been engaged in a deep study of the corrective properties of systems of residual classes (SRC), the bases of which are not mutually prime numbers. Such a system has certain corrective properties, which makes it necessary to assess the possibility and feasibility of using CMNPB to increase the reliability of computing in computer systems (CS). For the purpose of further research and development of CMNPB, we will consider a number of scientific statements, the use of the results of which will allow us to more fully study the corrective properties of codes with non-prime bases. Algorithms for monitoring and correcting errors in the SRC with mutually non-prime in pairs bases have been developed. Using these algorithms makes it relatively easy to implement a procedure for detecting and correcting one-time errors. Note that by the simplicity of the design of the decoder circuits, CMNPB have no analogues in the positional number systems. This is achieved by limiting the class of possible correctable errors, by introducing additional hardware redundancy in the representation of code words.