A novel method for computation of the discrete Fourier transform over characteristic two finite field of even extension degree

TL;DR

This paper introduces a new method for computing the discrete Fourier transform over finite fields of even extension degree, significantly reducing multiplicative complexity and optimizing cyclic convolution calculations.

Contribution

The paper presents a novel, optimal method for DFT computation over characteristic two finite fields with reduced multiplicative complexity and a constructive approach for cyclic convolution.

Findings

Reduces multiplicative complexity in DFT over finite fields

Provides a constructive method for cyclic convolution

Identifies the best known method for even extension degree fields

Abstract

A novel method for computation of the discrete Fourier transform over a finite field with reduced multiplicative complexity is described. If the number of multiplications is to be minimized, then the novel method for the finite field of even extension degree is the best known method of the discrete Fourier transform computation. A constructive method of constructing for a cyclic convolution over a finite field is introduced.