On the Compositions of Constant-Weight Codes for the Synthesis of Self-Checking and Controllable Digital Devices
Abstract
The paper is devoted to enumerating noise-resistant compositions of constant-weight codes with small values of the number of digits in codewords. The principles for identifying such compositions of constant-weight codes are established. Some of their characteristics of error detection in codewords are determined. In addition, special compositions of constant-weight codes are distinguished, the codewords of which are divided into pairs orthogonal in all bits. The use of such codes is effective in the synthesis of self-checking and controllable discrete devices according to two diagnostic features: belonging to the codewords of a given composition and belonging of the functions calculated in the concurrent error-detection circuits to the class of self-dual Boolean functions. The paper identifies two compositions with four bits in codewords that have this property. Compact structures of their self-checking checkers are given, and test vectors for them are indicated. The results obtained in the research of the authors of this paper can be effectively used in the construction of digital devices and systems for the detection of faults and errors in calculations.