Unidirectional Byte Error Correcting Codes for q-Ary Data

Christian Deppe

Jos H. Weber

L.S. Bobrow, S. L. Hakimi

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.

Ilya Vorobyev, В. В. Лебедев, Alexey Lebedev

In this paper, the problem of correction of a single error in q-ary symmetric channel with noiseless feedback is considered. We propose an algorithm to construct codes with feedback inductively. For all prime power q we prove that two instances of feedback are sufficient to transmit over the q-ary symmetric channel the same number of messages as in the case of complete feedback. Our other contribution is the construction of codes with one-time feedback with the same parameters as Hamming codes for q that is not a prime power. We also construct single-error-correcting codes with one-time feedback of size qn−2for arbitrary q and n ≤ q + 1, which can be seen as an analog for Reed-Solomon codes.

S. Wainberg