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Weight-Based Sum Codes with Arbitrary Modulus

Binary redundant codes are widely used in the synthesis of self-checking and fault-tolerant digital computing systems. Their use allows reducing the added redundancy to ensure self-checking and fault tolerance. The authors present the study results of a comprehensive sum codes class. When constructing such codes, predetermined sequences of weight coefficients and a summation procedure in the residue ring by the specified modulus are used. As an example, codes with two sequences of weight coefficients are considered: 1) natural series; 2) natural series except for powers of number 2. Previously unknown characteristics of error detection by codes in terms of multiplicities and types (unidirectional, symmetrical and asymmetrical) are established. The conditions for constructing noise-immune codes and methods for modifying codes to endow them with noise-immunity properties are given. The results of experiments on analysing the detecting abilities of sum codes when used to test errors at the outputs of combinational benchmarks are provided.