Abstract
The trace representation of sequences is a powerful tool for the analysis and for the design of pseudorandom sequences. Z. Dai et al. (2011) reduce the problem of determining trace representation of series of binary eth power residue sequences to that of determining the values of generating polynomials of cyclotomic classes. We derive the values of generating polynomials of cyclotomic classes of order 4, 6, 8 and consequently solve three problems pointed by Z. Dai et al. In fact, we study the discrete Fourier transform of cyclotomic sequences of order 4, 6, 8.
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A post-publication change was made to this article on 15 Jan 2020 to correct a grant number in the Acknowledgments.