Partial Spread and Vectorial Generalized Bent Functions

Thor Martinsen; Wilfried Meidl; Pantelimon Stanica

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arXiv · 1511.01705

Partial Spread and Vectorial Generalized Bent Functions

Thor Martinsen·Wilfried Meidl·Pantelimon Stanica

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Abstract

In this paper we generalize the partial spread class and completely describe it for generalized Boolean functions from $\F_2^n$ to $\mathbb{Z}_{2^t}$. Explicitly, we describe gbent functions from $\F_2^n$ to $\mathbb{Z}_{2^t}$, which can be seen as a gbent version of Dillon's $PS_{ap}$ class. For the first time, we also introduce the concept of a vectorial gbent function from $\F_2^n$ to $\Z_q^m$, and determine the maximal value which $m$ can attain for the case $q=2^t$. Finally we point to a relation between vectorial gbent functions and relative difference sets.

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Thor Martinsen, Wilfried Meidl, Pantelimon Stanica. 2015-11-05. Partial Spread and Vectorial Generalized Bent Functions. https://arxiv.org/abs/1511.01705

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