Time domain decoding of extended Reed-Solomon codes
L.L. Joiner, John Joseph Komo · 2002
Time domain decoding of extended and doubly extended Reed-Solomon codes are considered for both errors only decoding and errors and erasures decoding. The parity check and generator matrices are given for the singly and doubly extended Reed-Solomon codes in terms of the parity check and generator matrices of the Reed-Solomon codes. Syndrome calculations for the singly and doubly extended codes are discussed and the modifications necessary for the error location and error magnitude calculations are given. The modifications necessary for decoding extended Reed-Solomon codes using the Berlekamp-Massey algorithm and Euclid's algorithm for finding the error magnitudes are presented for both errors only and errors and erasures decoding.