Cutset codes augmented by Hakimi and Frank's technique are shown to be two-step orthogonalizable and, hence, two-step majority decodable. It is seen that these codes can also be decoded by decoders that have virtually the same amount of hardware as completely orthogonalizable codes with the same dimension.

This correspondence formulatesGF(q)matrix descriptions for a class of weighted, directed graphs. As a result of this formulation, the concept of graph theoretic error-correcting codes is generalized to theq-ary case. It is shown that graph theoreticq-ary codes are completely orthogonalizable and, hence, one-step majority decodable. It is also seen that known techniques for the augmentation of circuit codes can he extended to theq-ary case. The resulting codes remain easily decodable.