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In this work we present a new way to construct 3-resilient Boolean functions of 9 variables with nonlinearity 240. Such function have been discovered very recently in [1] and [2] by a heuristic search. We find these functions by an exhaustive search in the class of functions symmetric under cyclic shifts of the first seven variables. The exhaustive search was reduced significantly by using of special techniques and algorithms which can be helpful in other similar problems. Also we construct some new functions that attain the upper bound on nonlinearity of higher number of variables.
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