Abstract
It is proved that the maximal possible nonlinearity of nvariable m-resilient Boolean function is (Formula Presented.). This value can be achieved only for optimized functions (i. e. functions with an algebraic degree n − m − 1). For (Formula Presented.) it is suggested a method to construct an n-variable m-resilient function with maximal possible nonlinearity (Formula Presented.) such that each variable presents in ANF of this function in some term of maximal possible length n − m − 1.
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Tarannikov, Y. V. (2000). On resilient boolean functions with maximal possible nonlinearity. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1977, pp. 19–30). Springer Verlag. https://doi.org/10.1007/3-540-44495-5_3
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