Generalized bent functions and their Gray images

Abstract

In this paper we proved that generalized bent (gbent) functions defined on Z (n/2) with values in Z(2k) are regular and find connections between the (generalized) Walsh spectrum of these function and their components. We comprehensively characterize generalized bent and semibent functions with values in Z(16), which extends earlier results on gbent function with values in Z(4) and Z(8). We also show that the Gray images of gbent functions with values in (2k) are semibent/plateaued when k = 3,4.