Harmonic analysis of binary functions

Abstract

In this paper we introduce the two-modular Fourier transform of a binary function f : R → R defined over a finite commutative ring R = F2[X]/φ(X), where F2[X] is the ring of polynomials with binary coefficients and φ(X) is a polynomial of degree n, which is not a multiple of X. We also introduce the corresponding inverse Fourier transform. We then prove the corresponding convolution theorem.