Codes With Summation of Weight Coefficients of Data Vector Bits in the Ring of Residues Modulo an Arbitrary for Digital Computing Devices

Abstract

We consider the specificities of codes with the summation of weight coefficients of data vector bits in the ring of residues modulo an arbitrary. There’re established the characteristics of error detection by the given code class and some legitimacies related to the use of modules of particular values and of weight coefficients. It’s shown that the number of various weight-based sum codes is limited, nevertheless, large number of various ways of their formation exists for each value of bit number in data vectors. There’re given the algorithm to obtain bits of check vectors of being considered codes and the examples of their upbuilding; the way to calculate the number of not being revealed errors in data vectors is described. There’re defined the properties of weight-based sum codes of data vectors in the ring of residues modulo an arbitrary accounting for which may be useful while the settlement of technical diagnostics task, the synthesis of being selfchecking and fault-tolerant digital devices and devices with testability structures. The approach to the synthesis of coders of any weight-based sum codes on the base of binary number summators according to established module is described. There’re given some results of experiments on the analysis of revealing capacities of being considered codes in the circuits of inbuilt control of combinational benchmarks. Obtained in the work results are of universal character and not oriented to application just with one element base of being realized devices that make them useful not just at the moment but in the future.