Semi-Fast Fourier Transforms over GF(2m).

An algorithm which computes the Fourier transform of a sequence of length n over GF(2
^m
) using approximately 2nm multiplications and n
²
+ nm additions is developed. The number of multiplications is thus considerably smaller than the n
²
multiplications required for a direct evaluation, though the number of additions is slightly larger. Unlike the fast Fourier transform, this method does not depend on the factors of n and can be used when n is not highly composite or is a prime.