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Linear codes in generalized construction of resilient functions with very high nonlinearity

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2 Author(s)
E. Pasalic ; Dept. of Inf. Technol., Lund Univ., Sweden ; S. Maitra

We provide a new generalized construction method for highly nonlinear t-resilient functions, F:F2n→ F2m. The construction is based on the use of linear error-correcting codes together with highly nonlinear multiple output 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 very high nonlinearity for n>u. The method provides the currently best known nonlinearity results for most of the cases.

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IEEE Transactions on Information Theory  (Volume:48 ,  Issue: 8 )