An improvement on decoding of the binary systematic (47, 24, 11) quadratic residue code

An improved algebraic decoding algorithm (ADA) is presented to decode up to five possible errors in a binary systematic (47, 24, 11) quadratic residue (QR) code. The main idea of the improved ADA is to find out the new conditions in four-error and five-error cases and the smallest degree of the unknown syndrome polynomial in five-error case. Thus, the computational complexity in the finite field can be reduced. A simulation result shows that the decoding speed of the proposed ADA is faster than other existing ADAs.