Decoding of second order Reed-Muller codes with a large number of errors

Second order Reed-Muller codes are considered over a binary symmetric channel. We present a modified version of V.M Sidel´nikov and A.S. Pershakov algorithm, Problemy Peredachi Informatsii 1992, that has complexity of order n²log(n). Experimental results show that the algorithm corrects most error patterns of weight up to n/2(1-e) given that e exceeds n-1/3. This outperforms other decoding algorithms known for RM codes. Decoding performance for known algorithms has been evaluated and the results correspond to asymptotic performance for these algorithms.