Decoding the (41,20,10) Quadratic Residue Code Beyond its Error-Correcting Capability
J. Carmelo Interlando, Cynthia Padilla · 2011
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, 94B35