On Algebraic Decoding of Some Maximal Quaternary Codes and the Binary Golay Code

The quaternary codes devised in [Probl. Inf. Trans., 14, No. 2, 174–181 (1978)] have minimum distance $d=5$. As was shown there, they can be decoded using a standard syndrome decoding algorithm. In the present paper, we derive a simple algebraic criterion to determine the number of errors occurred and reformulate the earlier decoding algorithm described in the paper mentioned. Since a [12,6,6] quaternary code yields a cascade description of a binary extended [24,12,8] Golay code, this description provides a new method for decoding binary Golay codes.