  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.
