In this paper we prove that generalized bent (gbent) functions defined on $\mathbb{ Z}_2^n$ with values in $\mathbb{ Z}_{ 2^k}$ are regular, and find connections between the (generalized) Walsh spectrum of these functions and their components. We comprehensively characterize generalized bent and semibent functions with values in $\mathbb{ Z}_{ 16}$, which extends earlier results on gbent functions with values in $\mathbb{ Z}_4$ and $\mathbb{ Z}_8$. We also show that the Gray images of gbent functions with values in $\mathbb{ Z}_{ 2^k}$ are semibent/plateaued when $k=3,4$.
Categories: cs.IT math.IT