Generalized Partially Bent Functions

Based on the definition of generalized partially bent functions, using the theory of linear transformations, the relationship between generalized partially Bent functions over ring Z_N and generalized bent functions over ring Z_N is discussed. Assume that N is a prime number, it is proved that some generalized partially Bent functions can be decomposed as the addition of a generalized bent function and an affine function. The decomposition facilitates the easy understanding and construction of partially Bent functions and generalized partially Bent functions. The result obtained here generalizes the main work concerning partially Bent functions by Claud Carlet. Finally, an approach to construct generalized Bent functions using the Rudin-Shapiro construction is derived.