Welcome to the resource topic for 2023/1458
Title:
A Further Study of Vectorial Dual-Bent Functions
Authors: Jiaxin Wang, Fang-Wei Fu, Yadi Wei, Jing Yang
Abstract:Vectorial dual-bent functions have recently attracted some researchers’ interest as they play a significant role in constructing partial difference sets, association schemes, bent partitions and linear codes. In this paper, we further study vectorial dual-bent functions F: V_{n}^{(p)}\rightarrow V_{m}^{(p)}, where 2\leq m \leq \frac{n}{2}, V_{n}^{(p)} denotes an n-dimensional vector space over the prime field \mathbb{F}_{p}. We give new characterizations of certain vectorial dual-bent functions (called vectorial dual-bent functions with Condition A) in terms of amorphic association schemes, linear codes and generalized Hadamard matrices, respectively. When p=2, we characterize vectorial dual-bent functions with Condition A in terms of bent partitions. Furthermore, we characterize certain bent partitions in terms of amorphic association schemes, linear codes and generalized Hadamard matrices, respectively. For general vectorial dual-bent functions F: V_{n}^{(p)}\rightarrow V_{m}^{(p)} with F(0)=0, F(x)=F(-x) and 2\leq m \leq \frac{n}{2}, we give a necessary and sufficient condition on constructing association schemes. Based on such a result, more association schemes are constructed from vectorial dual-bent functions.
ePrint: https://eprint.iacr.org/2023/1458
See all topics related to this paper.
Feel free to post resources that are related to this paper below.
Example resources include: implementations, explanation materials, talks, slides, links to previous discussions on other websites.
For more information, see the rules for Resource Topics .