  A new transform over finite fields, the finite field Hartley transform
(FFHT), was recently introduced and a number of promising applications on the
design of efficient multiple access systems and multilevel spread spectrum
sequences were proposed. The FFHT exhibits interesting symmetries, which are
exploited to derive tailored fast transform algorithms. The proposed fast
algorithms are based on successive decompositions of the FFHT by means of
Hadamard-Walsh transforms (HWT). The introduced decompositions meet the lower
bound on the multiplicative complexity for all the cases investigated. The
complexity of the new algorithms is compared with that of traditional
algorithms.
