Paper 2023/1458
A Further Study of Vectorial Dual-Bent Functions
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.
Metadata
- Available format(s)
- Category
- Foundations
- Publication info
- Preprint.
- Keywords
- Vectorial dual-bent functionsAssociation schemesGeneralized Hadamard matricesLinear codesBent partitionsPartial difference sets
- Contact author(s)
-
wjiaxin @ mail nankai edu cn
fwfu @ nankai edu cn
wydecho @ mail nankai edu cn
yangjing @ sz tsinghua edu cn - History
- 2023-09-24: approved
- 2023-09-23: received
- See all versions
- Short URL
- https://ia.cr/2023/1458
- License
-
CC0
BibTeX
@misc{cryptoeprint:2023/1458, author = {Jiaxin Wang and Fang-Wei Fu and Yadi Wei and Jing Yang}, title = {A Further Study of Vectorial Dual-Bent Functions}, howpublished = {Cryptology {ePrint} Archive, Paper 2023/1458}, year = {2023}, url = {https://eprint.iacr.org/2023/1458} }