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

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2 Author(s)
Wang, Y. ; Dept. of Electr. & Comput. Eng., California Univ., Santa Barbara, CA, USA ; Zhu, X.

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(pm) is introduced. It requires only O(n(log n)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

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Selected Areas in Communications, IEEE Journal on  (Volume:6 ,  Issue: 3 )