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Computer Science > Information Theory

arXiv:2211.11516 (cs)
[Submitted on 15 Nov 2022]

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

Authors: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}.
Subjects: Information Theory (cs.IT); Cryptography and Security (cs.CR)
Cite as: arXiv:2211.11516 [cs.IT]
  (or arXiv:2211.11516v1 [cs.IT] for this version)
  https://doi.org/10.48550/arXiv.2211.11516

Submission history

From: Amar Bapić [view email]
[v1] Tue, 15 Nov 2022 11:15:52 UTC (11 KB)
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