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.

翻译：向量对偶弯曲函数因其在构造部分差集、结合方案、弯曲划分和线性码中的重要作用，近年来引起了一些研究者的兴趣。本文进一步研究了向量对偶弯曲函数 $F: V_{n}^{(p)}\rightarrow V_{m}^{(p)}$，其中 $2\leq m \leq \frac{n}{2}$，$V_{n}^{(p)}$ 表示素域 $\mathbb{F}_{p}$ 上的 $n$ 维向量空间。我们分别从无定形结合方案、线性码和广义Hadamard矩阵的角度，给出了某些向量对偶弯曲函数（称为满足条件A的向量对偶弯曲函数）的新刻画。当 $p=2$ 时，我们从弯曲划分的角度刻画了满足条件A的向量对偶弯曲函数。此外，我们还分别从无定形结合方案、线性码和广义Hadamard矩阵的角度，刻画了某些弯曲划分。对于满足 $F(0)=0, F(x)=F(-x)$ 且 $2\leq m \leq \frac{n}{2}$ 的一般向量对偶弯曲函数 $F: V_{n}^{(p)}\rightarrow V_{m}^{(p)}$，我们给出了构造结合方案的充分必要条件。基于这一结果，我们利用向量对偶弯曲函数构造了更多的结合方案。