Generalized bent functions and their Gray images

Abstract

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 $k=3,4$.

Cited by in corpus (4)

• Partial Spread and Vectorial Generalized Bent Functions
• ${\mathbb{Z}}_q$-valued generalized bent functions in odd characteristics
• Construction methods for generalized bent functions
• More characterizations of generalized bent function in odd characteristic, their dual and the gray image