An efficient prime-length DFT algorithm over finite fields GF(2m)

Abstract

This letter describes a discrete Fourier transform (DFT) for prime transform lengths N ≥ 3, where the sample values are elements of finite (Galois) fields GF(2m). A regular and uniform system of additions and multiplications is presented which reduces the multiplicative complexity by at least one-quarter, compared with a brute-force implementation. The benefits of the algorithm are shown with respect to BCH decoding; in particular, the efficient computation of syndromes will be discussed. Copyright © 2003 AEI.