Modulo codes with summation of weighted transitions with natural number sequence of weights

Systematic codes with simple formation rules and low redundancy are used in the reliable digital systems design. Codes with summation with a constant number of check bits, which does not depend on data vector length, are often applied. The paper shows that error detection properties of these codes could be improved by a modification of check bits calculation rules. The authors offer the algorithm of the formation of a code with summation based on weighing the transitions between bits on neighboring positions of data vectors and calculation of the total weight of the data vector by the modulo, which is degree of two. The paper contains a detailed analysis of properties of new codes compared with known ones. The authors state the conditions of the formation of error-tolerant modulo weight-based codes with summation with the maximum number of detected errors in data vectors. Improving of error detection characteristics in new codes, compared with classic ones, is achieved by the uniform distribution of data vectors among check vectors. This, in its turn, brings some part of monotonous and asymmetric errors to the class of undetectable in addition to symmetric ones. Modulo weight-based codes detect more symmetric errors than modulo codes with summation of ones, but asymmetric errors are the dominant sort of them for almost any length of data vector. Modulo codes with summation of weighted transitions are the perspective class of systematic codes to solve the tasks of digital systems technical diagnostics.