On the decoding of the (24, 12, 8) Golay code

An improved syndrome shift-register decoding algorithm, called the syndrome-weight decoding algorithm, is proposed for decoding three possible errors and detecting four errors in the (24, 12, 8) Golay code. This method can also be extended to decode two other short codes, such as the (15, 5, 7) cyclic code and the (31, 16, 7) quadratic residue (QR) code. The proposed decoding algorithm makes use of the properties of cyclic codes, the weight of syndrome, and the syndrome decoder with a reduced-size lookup table (RSLT) in order to reduce the number of syndromes and their corresponding coset leaders. This approach results in a significant reduction in the memory requirement for the lookup table, thereby yielding a faster decoding algorithm. Simulation results show that the decoding speed of the proposed algorithm is approximately 3.6 times faster than that of the algebraic decoding algorithm.