Ternary Parity Codes: Features
Д.В. Ефанов · 2019
For organizing offline and online diagnostics systems, redundant coding is widely used. Codes are focused on error detection in the codeword bits. At present, the automation devices function in binary logic and consequently binary redundant codes are used in the development of technical diagnostic tools. Nevertheless, several specialists note the ternary number system and automation devices advantage that implement its principles. This work is devoted to the simplest ternary codes - ternary parity codes. Some ternary parity codes properties are described, and the need for a more detailed account of the error type in the ternary redundant code's data vectors is noted. It is proved that the described ternary parity code, built based on using a single convolution function modulo three, has the data vectors uniform distribution property between check single-trit vectors. In addition, was introduced the concept of code with the least total number of undetectable errors in the ternary code data vectors for the lengths fixed values of data and check vectors. It is proved that such a code has an data vectors uniform distribution between all possible check vectors. Formulas for calculating the total number of undetectable errors in such codes are given.