Decoding the binary Golay code with miracle octad generators (Corresp.)

The recently introduced notion of a miracle octad generator can be viewed as a means of identifying a codeword of weight eight of the extended binary Golay code, given five of its nonzero positions. It is shown that this fact can be used as the basis of a new decoding algorithm for this code which decodes all the information positions simultaneously. The performance of this algorithm, as well as methods for its implementation, are considered.