A fast algorithm for the Fourier transform over finite fields and its VLSI implementation

Abstract

The Fourier transform over finite fields is mainly required in the encoding and decoding of Reed-Solomon and BCH codes. An algorithm for computing the Fourier transform over any finite field GF(p/sup m/) is introduced. It requires only O(n(log n)/sup 2//4) additions and the same number of multiplications for an n-point transform and allows in some fields a further reduction of the number of multiplications to O(n log n). Because of its highly regular structure, this algorithm can be easily implementation by VLSI technology. >