Fourier Transforms and the 2-adic Span of Periodic Binary Sequences

IEEE Transactions on Information Theory 46 (2000) 687-691.

Andrew Klapper, 779A Anderson Hall, Dept. of Computer Science, University of Kentucky, Lexington, KY, 40506-0046, klapper at
Mark Goresky, Institute for Advanced Study
Lawrence Washington, University of Maryland

Abstract An arithmetic or with-carry analog of Blahut's theorem is presented. This relates the length of the smallest feedback with carry shift register to the number of nonzero classical Fourier coefficients of a periodic binary sequence.

Index Terms -- Periodic binary sequence; feedback register; Fourier coefficients; Blahut's theorem; 2-adic numbers.