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Best linear approximation and correlation immunity of functions over Zm*

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3 Author(s)
Jinjun Zhou ; Dept. of Appl. Math., Zhengzhou Inf. Eng. Inst., China ; Weihong Chen ; Fengxiu Gao

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 ρf(x), the best linear approximation of a function f(x) can be easily obtained when the codomain of f(x) is Zm. A spectral characterization of correlation-immune functions over Z, is also presented in terms of the DFT of ζf(x)

Published in:

IEEE Transactions on Information Theory  (Volume:45 ,  Issue: 1 )