Abstract
This correspondence formulates <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">GF(q)</tex> 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 the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</tex> -ary case. It is shown that graph theoretic <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</tex> -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 the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</tex> -ary case. The resulting codes remain easily decodable.
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