Connections between quaternary and boolean bent functions

This work is related to quaternary bent functions f : Zn ^ Z₄. The relation between Walsh - Hadamard transform coefficients of quaternary and two Boolean functions is explored. It is proved that any quaternary bent function is a regular bent function for any n. The number of quaternary bent functions in one and two variables is counted. For quaternary bent function in one variable g(x + 2y) = a(x,y) + 2b(x,y), it is proved that b and a ф b are Boolean bent functions, where x,y £ Z₂. Properties of Boolean functions a, b and a ф b in representation of quaternary bent function in two variables as g(x + 2y) = a(x,y) + 2b(x,y) are described.

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