Triple Modular Sum Code as a New Code for the Tasks of Checkable Automation System Synthesis

Abstract

The author developed a new method of building a code with sum of unit data bits. It was suggested to calculate modified weight of a data bit, when building a sum code. The latter was achieved by determining the least non-negative residue of its actual weight, by means of a predefined module. Then the obtained number was corrected using two correction factors, calculated as modulo two convolution of various subsets of data vector bits. The author called the new code a triple modular sum code. The triple modular code is compared to classical Berger code according to its redundancy. It should be mentioned that it has better characteristics of error detection in data vectors in comparison with Berger code. Triple modular sum codes extend the class of common codes with low redundancy. Their application can be justified by hardware costs on implementation of fault detection property in controlled discrete objects. In this case, it is possible to build a whole family of triple modular codes for one length value of a data vector, thus extending the prospects of their application in the process of building reliable and safe control components.