Constructions of 2-resilient rotation symmetric Boolean functions through symbol transformations of cyclic Hadamard matrix.

In this paper, the properties of symbol transformations of cyclic Hadamard matrices are studied. An infinite class of (n − 1) -variable 2-resilient rotation symmetric Boolean functions are constructed, and the nonlinearity of the constructed functions is 2 n (n − 1). The crucial technique of this method is to determine a subset T ⊆ F 2 n − 1 satisfying a correspondent condition. This is a new construction of 2-resilient rotation symmetric Boolean functions via switching the supports of (n − 1) -variable rotation symmetric Boolean functions of degree one, i.e., f 0 n − 1 (x 1 , x 2 , ⋯ , x n − 1) = ⊕ i = 1 n − 1 x i , where n = 4 t. [ABSTRACT FROM AUTHOR]