Paper 2023/1458

A Further Study of Vectorial Dual-Bent Functions

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.

Metadata
Available format(s)
PDF
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
No rights reserved
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}
}
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