NASA NTRS · 19780031910
High-radix transforms for Reed-Solomon codes over Fermat primes
Abstract
A method is proposed to streamline the transform decoding algorithm for Reed-Solomon (RS) codes of length equal to 2 raised to the power 2n. It is shown that a high-radix fast Fourier transform (FFT) type algorithm with generator equal to 3 on GF(F sub n), where F sub n is a Fermat prime, can be used to decode RS codes of this length. For a 256-symbol RS code, a radix 4 and radix 16 FFT over GF(F sub 3) require, respectively, 30 and 70% fewer modulo F sub n multiplications than the usual radix 2 FFT.
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Liu, K. Y., Reed, I. S., Truong, T. K.. 1977-11-01. High-radix transforms for Reed-Solomon codes over Fermat primes. https://ntrs.nasa.gov/citations/19780031910
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