Best linear approximation and correlation immunity of functions over Zm*

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