Abstract
In this paper we provide a new generalized construction method of highly nonlinear t-resilient functions, F : \( \mathbb{F}_2^n \mapsto \mathbb{F}_2^m \). 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 \( 2^{n - 1} - 2^{\left\lceil {\frac{{n + u - m - 1}} {2}} \right\rceil } \) for n ≥ u + 3m. The method provides currently best known nonlinearity results.
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Pasalic, E., Maitra, S. (2001). Linear Codes in Constructing Resilient Functions with High Nonlinearity. In: Vaudenay, S., Youssef, A.M. (eds) Selected Areas in Cryptography. SAC 2001. Lecture Notes in Computer Science, vol 2259. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45537-X_5
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