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

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

Andrew Klapper, 779A Anderson Hall, Dept. of Computer Science,
University of Kentucky, Lexington, KY, 40506-0046, klapper at cs.uky.edu.
www.cs.uky.edu/~klapper/andy.html

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.