Generalized bent functions and their Gray images

Thor Martinsen; Wilfried Meidl; Pantelimon Stanica

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arXiv · 1511.01438

Generalized bent functions and their Gray images

Thor Martinsen·Wilfried Meidl·Pantelimon Stanica

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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 $k=3,4$.

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Thor Martinsen, Wilfried Meidl, Pantelimon Stanica. 2015-11-04. Generalized bent functions and their Gray images. https://arxiv.org/abs/1511.01438

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