Connections between quaternary and component boolean bent functions

This paper is about quaternary bent functions. Function д : Zn ^ Z₄ is called quaternary in n variables. It was proven that bentness of a quaternary function g(x + 2y) = a(x, y) + 2b(x, y) doesn't directly depend on the bentness of Boolean functions b and a ф b. The number of quaternary bent functions in one and two variables is obtained with a description of properties of Boolean functions b and a ф b. Two simple constructions of quaternary bent functions in any number of variables are pre- n sented. The first one is given by the formula g(x₁ + 2x_n+1,..., x_n + 2x_2n) = 2x_ix_i+_n + cxj, i=1 c Е Z₂ and j Е {1,... ,n}. The second construction allows one to get a bent function g'(x + 2y) = 3a(x, y) + 2b(x, y), where g(x + 2y) = a(x, y) + 2b(x, y) is bent.

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