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Fast transform for decoding both errors and erasures of Reed-Solomon codes over GF(2m) for 8≤m≤10

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4 Author(s)
Truong, T.K. ; Dept. of Inf. Eng., I-Shou Univ., Ta-Hsu Hsiang, Taiwan ; Chen, P.D. ; Wang, L.J. ; Cheng, T.C.

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 2m-1 points over GF(2m), where 8≤m≤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 2m-1 over GF(2m) for 8≤m≤10 is reduced substantially from the previous time-domain decoder. A computer simulation verifies these new results.

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Communications, IEEE Transactions on  (Volume:54 ,  Issue: 2 )