A new inequality in discrete fourier theory
Michaël Quisquater, Bart Preneel, Joos P. L. Vandewalle · IEEE Transactions on Information Theory · 2003
Discrete Fourier theory has been applied successfully in digital communication theory. In this correspondence, we prove a new inequality linking the number of nonzero components of a complex valued function defined on a finite Abelian group to the number of nonzero components of its Fourier transform. We characterize the functions achieving equality. Finally, we compare this inequality applied to Boolean functions to the inequality arising from the minimal distance property of Reed-Muller codes.