Best linear approximation and correlation immunity of functions over Z*(m)

A fast algorithm for the computation of the rho-representation of n-dimensi onal discrete Fourier transform (DPT) is given, where rho is an mth primiti ve root of unity. Applying this algorithm to the standard rho-representatio n of the DFT of rho(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(m) is al so presented in terms of the DFT of zeta(f(x)).