2022/02/08 by Jiaxin Wang, Wang, Jiaxin, Fang‐Wei Fu +1 · 2 citations
Computer Science · Social Sciences · #Coding theory and cryptography #FOS: Computer and information sciences #Information Theory (cs.IT) #Islamic Finance and Communication
paper · pdf · doi:10.48550/arxiv.2202.03817
openalex publication_date 2022/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Bent functions f: Vn→ \mathbbFp with certain additional properties play an important role in constructing partial difference sets, where Vn denotes an n-dimensional vector space over \mathbbFp, p is an odd prime. In \citeCesmelioglu1,Cesmelioglu2, the so-called vectorial dual-bent functions are considered to construct partial difference sets. In \citeCesmelioglu1, Çeşmelioǧlu et al. showed that for vectorial dual-bent functions F: Vn→ Vs with certain additional properties, the preimage set of 0 for F forms a partial difference set. In \citeCesmelioglu2, Çeşmelioǧlu et al. showed that for a class of Maiorana-McFarland vectorial dual-bent functions F: Vn→ \mathbbFps, the preimage set of the squares (non-squares) in \mathbbFps* for F forms a partial difference set. In this paper, we further study vectorial dual-bent functions and partial difference sets. We prove that for vectorial dual-bent functions F: Vn→ \mathbbFps with certain additional properties, the preimage set of the squares (non-squares) in \mathbbFps* for F and the preimage set of any coset of some subgroup of \mathbbFps* for F form partial difference sets. Furthermore, explicit constructions of partial difference sets are yielded from some (non)-quadratic vectorial dual-bent functions. In this paper, we illustrate that almost all the results of using weakly regular p-ary bent functions to construct partial difference sets are special cases of our results.