The Fast Decoding of Reed-Solomon Codes Using High-Radix Fermat Theoretic Transforms
K. Y. Liu, I.S. Reed, Trieu‐Kien Truong · Deep Space Network Progress Report · 1976
Fourier-like transforms over GF(F sub n), where F sub n = 2(2n) + 1 is a Fermat prime, are applied in decoding Reed-Solomon codes. It is shown that such transforms can be computed using high-radix fast Fourier transform (FFT) algorithms requiring considerably fewer multiplications than the more usual radix 2 FFT algorithm. A special 256-symbol, 16-symbol-error-correcting, Reed-Solomon (RS) code for space communication-link applications can be encoded and decoded using this high-radix FFT algorithm over GF(F sub 3).