Research of Two-Modulus Weighted Codes with Summation Involving Arbitrary Partitions of Several Data Symbols
Annotatsiya
A method has been proposed for constructing two-modulus sum codes that are suitable for solving the synthesis problems of self-checking digital computing devices and systems, as well as the technical means of their diagnostics. In the process of constructing a code, a set of data symbols is divided into two subsets, forming separate vectors for which the total weight is calculated according to a predetermined modulus. Beforehand, in each of the selected vectors, one of the data symbols is weighted with a coefficient from a natural series. Codes obtained with different values of weight coefficients and modulus for determining the total weight form a separate family of uniform binary codes with a fixed number of check symbols. The article provides an example of constructing a sum codes in the ring of residues modulus M = 4. Using this modulus enables the construction of a two-modulus code with k = 4 check symbols for any value of the m number of data symbols. As the value of m increases, the relationship between the number of data symbols and check symbols will change significantly, and the resulting code will have low redundancy. This is important when using the considered class of codes in the construction of digital devices. Previously unknown properties of the discussed class of sum codes have been identified, and taking these into account is beneficial when addressing problems related to the synthesis and technical diagnostics of digital devices.