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It is shown that is an element of order in , where is a Fermat prime for . Hence it can be used to define a fast Fourier transform (FFT) of as many as symbols in . Since is a root of unity of order in , this transform requires fewer muitiplications than the conventional FFT algorithm. Moreover, as Justesen points out , such an FFT can be used to decode certain Reed-Solomon codes. An example of such a transform decoder for the case , where is in , is given.