Best Linear Approximation and Correlation Immunity of Functions Over Z*m

Abstract

A fast algorithm for the computation of the /spl rho/-representation of n-dimensional discrete Fourier transform (DFT) is given, where /spl rho/ is an mth primitive root of unity. Applying this algorithm to the standard /spl rho/-representation of the DFT of /spl rho//sup f(x)/, the best linear approximation of a function f(x) can be easily obtained when the codomain of f(x) is Z/sub m/. A spectral characterization of correlation-immune functions over Z, is also presented in terms of the DFT of /spl zeta//sup f(x)/.