  In this study, we consider the Euclidean and Galois hulls of multi-twisted
(MT) codes over a finite field $\mathbb{F}_{p^e}$ of characteristic $p$. Let
$\mathbf{G}$ be a generator polynomial matrix (GPM) of a MT code $\mathcal{C}$.
For any $0\le \kappa<e$, the $\kappa$-Galois hull of $\mathcal{C}$, denoted by
$h_\kappa\left(\mathcal{C}\right)$, is the intersection of $\mathcal{C}$ with
its $\kappa$-Galois dual. The main result in this paper is that a GPM for
$h_\kappa\left(\mathcal{C}\right)$ has been obtained from $\mathbf{G}$. We
start by associating a linear code $\mathcal{Q}_\mathbf{G}$ with $\mathbf{G}$.
We show that $\mathcal{Q}_\mathbf{G}$ is quasi-cyclic. In addition, we prove
that the dimension of $h_\kappa\left(\mathcal{C}\right)$ is the difference
between the dimension of $\mathcal{C}$ and that of $\mathcal{Q}_\mathbf{G}$.
Thus the determinantal divisors are used to derive a formula for the dimension
of $h_\kappa\left(\mathcal{C}\right)$. Finally, we deduce a GPM formula for
$h_\kappa\left(\mathcal{C}\right)$. In particular, we handle the cases of
$\kappa$-Galois self-orthogonal and linear complementary dual MT codes; we
establish equivalent conditions that characterize these cases. Equivalent
results can be deduced immediately for the classes of cyclic, constacyclic,
quasi-cyclic, generalized quasi-cyclic, and quasi-twisted codes, because they
are all special cases of MT codes. Some numerical examples, containing optimal
and maximum distance separable codes, are used to illustrate the theoretical
results.
