Improvement on decoding of the (71, 36, 11) quadratic residue code

In this paper, a fast algebraic decoding algorithm (ADA) is proposed to correct all patterns of five errors or less in the binary systematic (71, 36, 11) quadratic residue (QR) code. The method is based on the modification of the ADAs developed by Reed et al and Lin et al. The new conditions and the error-locator polynomials for decoding this code will be derived. Besides, a computer search shows that the minimum degree of the unknown syndrome polynomial f(S₇) in the five-error case is 2. Hence, the computational complexity can be reduced in finite field. Simulation result shows that the average decoding time of the proposed ADA is superior to the ADA given by Chang et al.