Fast Transform for Decoding Both Errors and Erasures of Reed – Solomon Codes Over GF ( 2 m ) for 8 m 10

In this letter, it is shown that a fast, prime-factor discrete Fourier transform (DFT) algorithm can be modified to compute Fourier-like transforms of long sequences of 2 1 points over GF(2 ), where 8 10. Using these transforms, together with the Berlekamp–Massey algorithm, the complexity of the transform-domain decoder for correcting both errors and erasures of the Reed–Solomon codes of block length 2 1 over GF(2 ) for 8 10 is reduced substantially from the previous time-domain decoder. A computer simulation verifies these new results.

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