Secondary constructions of vectorial $p$-ary weakly regular bent functions

Amar Bapić

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arXiv · 2211.11516

Secondary constructions of vectorial $p$-ary weakly regular bent functions

Amar Bapić

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Abstract

In \cite{Bapic, Tang, Zheng} a new method for the secondary construction of vectorial/Boolean bent functions via the so-called $(P_U)$ property was introduced. In 2018, Qi et al. generalized the methods in \cite{Tang} for the construction of $p$-ary weakly regular bent functions. The objective of this paper is to further generalize these constructions, following the ideas in \cite{Bapic, Zheng}, for secondary constructions of vectorial $p$-ary weakly regular bent and plateaued functions. We also present some infinite families of such functions via the $p$-ary Maiorana-McFarland class. Additionally, we give another characterization of the $(P_U)$ property for the $p$-ary case via second-order derivatives, as it was done for the Boolean case in \cite{Zheng}.

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Amar Bapić. 2022-11-15. Secondary constructions of vectorial $p$-ary weakly regular bent functions. https://arxiv.org/abs/2211.11516

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