Algebraic decoding of the binary systematic (71, 36, 11) quadratic residue code

Abstract

A fast and efficient algebraic decoding algorithm (ADA) is proposed to correct up to five possible error patterns in the binary systematic (71, 36, 11) quadratic residue (QR) code. The technique required here is based on the ADA developed by He et al. [2001. Decoding the (47, 24, 11) quadratic residue code. IEEE transactions on information theory, 47 (3), 1181–1186.] and the modification of the ADA developed by Lin et al. [2010. Decoding of the (31, 16, 7) quadratic residue code. Journal of the Chinese institute of engineers, 33 (4), 573–580; 2010. High speed decoding of the binary (47, 24, 11) quadratic residue code. Information sciences, 180 (20), 4060–4068]. The new proposed conditions and the error-locator polynomials for different numbers of errors in the received word are derived. Simulation results show that the decoding speed of the proposed ADA is faster than the other existing ADAs.