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A general explicit construction of bent functions is described, which unifies well known constructions due to Maiorana-McFarland and Dillon as two opposite extremal cases. Within this framework we also find new ways to generate bent functions. Then it is shown how the constructed bent functions can be modified in order to obtain highly nonlinear balanced Boolean functions. Although their nonlinearity is the best known so far, it remains open whether this bound can still be improved.

Construction of bent functions and balanced Boolean functions with high nonlinearity