Fast Algebraic Decoding of the (89, 45, 17) Quadratic Residue Code

In this letter, the algebraic decoding algorithm of the (89, 45, 17) binary quadratic residue (QR) code proposed by Truong et al. is modified by using the efficient determination algorithm of the primary unknown syndromes. The correctness of the proposed decoding algorithm is verified by computer simulations and the use of two corollaries. Also, simulation results show that the CPU time of this algorithm is approximately 4 times faster than that of the previously mentioned decoding algorithm at least. Therefore, such a fast decoding algorithm can now be applied to achieve efficiently the reliability-based decoding for the (89, 45, 17) QR code. Finally, the performance of its algebraic soft-decision decoder expressed in terms of the bit-error probability versus E_b/N₀ is given but not available in the literature.