Decoding of the (48, 24, 12) extended quadratic residue code up to six errors

This paper is to develop a modified algorithm for decoding the (48, 24, 12) binary quadratic residue code up to six errors. The technique in this paper uses the algebraic decoding algorithm for the (47, 24, 11) quadratic residue code offered by Truong et al. to correct up to five errors. Then, the technique of detecting a six-error is utilized. Finally, the reliability-search algorithm, proposed by Dubney et al., is applied for correcting the six-error. The computer simulation of the new scheme shows that at least 86% and 96% of weight-6 error patterns occurred are corrected if the E_b/N₀ ratios are greater than 3 dB and 6 dB, respectively.