Decoding of the (31, 16, 7) quadratic residue code
Tsung‐Ching Lin, Hsin‐Chiu Chang, Hung‐Peng Lee, Shao‐I Chu, Trieu‐Kien Truong · Journal of the Chinese Institute of Engineers · 2010
An algebraic decoding algorithm is proposed to correct all error patterns of up to three errors in the binary (31, 16, 7) Quadratic Residue (QR) code with reducible generator polynomial. The decoding technique, a modification of the decoding algorithm given by Reed et al., is based on the application of the decoding algorithm proposed by Truong et al. The computation of all syndromes is done in a small field, namely, GF(25). Thus, the computational complexity can be reduced. A full simulation shows that this novel decoding method is superior to the algebraic decoding algorithm given by Reed et al.