Necessary and sufficient conditions for design of completely checkable modulo $2$ convolution circuits

The paper is concerned with possibility of designing completely checkable modulo 2 convolution circuits incorporated into self-checking in-built control circuits incorporated into self-checking in-built control circuits with specified input totalities of a discrete device to be controlled. The output totalities are represented as tables. Table versions are considered with different numbers of rows and columns; the necessary and sufficient conditions for design of circuits are derived; an algorithm of their design is given.