**A new method for secondary constructions of vectorial bent functions**

*Amar Bapić and Enes Pasalic*

**Abstract: **In 2017, Tang et al. have introduced a generic construction for bent functions of the form $f(x)=g(x)+h(x)$, where $g$ is a bent function satisfying some conditions and $h$ is a Boolean function. Recently, Zheng et al. generalized this result to construct large classes of bent vectorial Boolean function from known ones in the form $F(x)=G(x)+h(X)$, where $G$ is a bent vectorial and $h$ a Boolean function. In this paper we further generalize this construction to obtain vectorial bent functions of the form $F(x)=G(x)+\mathbf{H}(X)$, where $\mathbf{H}$ is also a vectorial Boolean function. This allows us to construct new infinite families of vectorial bent functions, EA-inequivalent to $G$, which was used in the construction. Most notably, specifying $\mathbf{H } (x)=\mathbf{h} (Tr_1^n(u_1x),\ldots,Tr_1^n(u_tx))$, the function $\mathbf{h} :\mathbb{F}_2^t \rightarrow \mathbb{F}_{2^t}$ can be chosen arbitrary which gives a relatively large class of different functions for a fixed function $G$. We also propose a method of constructing vectorial $(n,n)$-functions having maximal number of bent components.

**Category / Keywords: **Bent functions, Vectorial bent functions, Algebraic degree, EA equivalence, CCZ equivalence, Maximal number of bent components

**Date: **received 27 Dec 2020, last revised 27 Dec 2020

**Contact author: **amar bapic at famnit upr si

**Available format(s): **PDF | BibTeX Citation

**Version: **20201227:132110 (All versions of this report)

**Short URL: **ia.cr/2020/1609

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