有限域上任意长度的DFT

Discrete Fourier Transform of Arbitrary Blocklength in Finite Fields

有限域上的ＤＦＴ在数字信号处理、纠错码和密码等领域都有重要应用；通常的有限域上ＤＦＴ仅限于长度与有限域特征互素的情形，它远远不能满足处理任意长度数据的需要．本文提出了有限域上任意长度的ＤＦＴ，研究了新变换的有关性质，并讨论了它在密码、编码中的应用．

Discrete Fourier Transform in finite fields has a wide range of applications,especially in digital signal processing,coding and cryptology.The conventional DFT in finite fields exists only for blocklength which is co-prime with the characteristics of the fields,so it can not be used to process the data with any other blocklengths.In this paper,a new DFT of arbitrary blocklength in finite fields is proposed,and the related properties of the new DFT are investigated,its applications in cryptology and coding are also discussed.