The quadratic residue codes are a class of the error correcting codes with interesting mathematics. Among them, the (31,
16, 7) quadratic residue code is the code with reducible generator polynomial and three-error-correcting capacity. The
algebraic decoding algorithm for the (32, 16, 8) quadratic residue code is developed by Reed et al. (1990). In this paper,
a simplified decoding algorithm is proposed. The algorithm uses bit-error probability estimates, which is first developed
by Reed MIT Lincoln Laboratory Report (1959), to cancel the third error and then uses the algebraic decoding algorithm
mentioned above to correct the remaining two errors. Simulation results show that this modified decoding algorithm
slightly reduces the decoding complexity for correcting the third error while maintaining the same BER performance in
additive white Gaussian noise (AWGN). Also, the flowchart of the above decoding algorithm is illustrated with Fig. 1.
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