Linear Codes in Constructing Resilient Functions with High Nonlinearity

In this paper we provide a new generalized construction method of highly nonlinear t-resilient functions, F : F2n → F2m. The construction is based on the use of linear error correcting codes together with multiple output bent functions. Given a linear [u, m, t + 1] code we show that it is possible to construct n-variable, m-output, t-resilient functions with nonlinearity 2n-1 - 2⌈n+u-m-1/2⌉ for n ≥ u + 3m. The method provides currently best known nonlinearity results.

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