and C.Padilla. Decoding the (41,20,10) Quadratic Residue Code Beyond its ErrorCorrecting Capability

Abstract An algebraic decoding algorithm for the expurgated quadratic residue code of length 41 is presented. The algorithm is guaranteed to produce the correct error-location polynomial whenever an error pattern of weight up to four occurs. An error pattern of weight five is not correctable if it is equidistant from the all-zero codeword and a codeword of weight ten. If an error pattern of weight five occurs, the algorithm will decide whether it is correctable; in the affirmative case, it will either produce the correct error-location polynomial or declare failure. However, the latter outcome, that is, failure, occurs with very low probability. Mathematics Subject Classification: 94B05, 94B15, 94B3