High-radix transforms for Reed-Solomon codes over Fermat primes (Corresp.)
Kwang Liu, I.S. Reed, Treiu-Kien Truong · IEEE Transactions on Information Theory · 1977
It is shown that a high-radix fast Fourier transform (FFT) with generator\gamma = 3over GF(F_{n}), whereF_{n} = 2^{2}^{n'} + 1is a Fermat prime, can be used for encoding and decoding of Reed-Solomon (RS) codes of length2^{2}^{n}. Such an RS decoder is considerably faster than a decoder using the usual radix 2 FFT. This technique applies most ideally to a 16-error-correcting, 256-symbol RS code of 8 bits being considered currently for space communication applications. This special code can be encoded and decoded rapidly using a high-radix FFT algorithm over GF(F_{3}).