Decoding the (31, 16, 7) quadratic residue code in GF(2^5)

The binary QR codes are well known for their good behavior. The proposed algebraic decoding algorithm for decoding the (31, 16, 7) QR code with reducible generator polynomial is able to correct up to three errors in the finite field GF(2⁵). The proposed algorithm is based on an application of the decoding algorithm given by Truong et al. and Chen et al. to modify the decoding algorithm proposed by Reed et al. All syndromes in the error-locator polynomial are computed in the finite field GF(2⁵). Thus, the decoding time can be reduced. Moreover, the simulation results for comparing the proposed decoding algorithm with decoding algorithm given by Reed et al. are given. This algorithm is suitable for implementation in a programmable microprocessor or special-purpose VLSI chip.