Compositions of two constant-weight codes with orthogonal combinations over all bits for self-checking discrete device design

This paper proposes using compositions of two constant-weight codes with orthogonal combinations over all bits in the design of controllable and self-checking discrete devices. With such codes, computation control at the outputs of discrete devices can be implemented via the attribute of belonging of the codewords to a given constant-weight code and, moreover, via the attribute of belonging of each function describing the codeword bits to the class of self-dual Boolean functions. It is shown how to construct noninterference codes based on the composition of two constant-weight codes with orthogonal combinations over all bits. Explicit formulas are derived to determine the number of errors undetectable by compositions of constant-weight codes by their types (by the number of erroneous 0s and 1s in codewords) and multiplicities. The properties of the codes under consideration are briefly described. The structure of concurrent error-detection circuits is presented for discrete devices based on the composition of two constant-weight codes with orthogonal combinations over all bits and computation control via two diagnostic attributes. The use of such compositions can be effective in building highly reliable discrete devices on various components.