Efficient Implementation of DFT over GF(qm)

In this paper an algorithm to compute N-point DFT over a finite field qm without multiplication is proposed, where q is a prime power and N is a positive integer not divisible by the characteristic of F_qm. The proposed method uses redundant representation for field elements and it is shown that no multiplication operations in F_q are required for computing N-point DFT. Both bit-serial and bit-parallel architectures to realize the algorithm are also presented that use only finite field adders and registers. One constrain of this method is that m must divide the multiplicative order of q mod N.