  In this paper, we study the algebraic structure of
$(\sigma,\delta)$-polycyclic codes, defined as submodules in the quotient
module $S/Sf$, where $S=R[x,\sigma,\delta]$ is the Ore extension ring, $f\in
S$, and $R$ is a finite but not necessarily commutative ring. We establish that
the Euclidean duals of $(\sigma,\delta)$-polycyclic codes are
$(\sigma,\delta)$-sequential codes. By using $(\sigma,\delta)$-Pseudo Linear
Transformation, we define the annihilator dual of $(\sigma,\delta)$-polycyclic
codes. Then, we demonstrate that the annihilator duals of
$(\sigma,\delta)$-polycyclic codes maintain their $(\sigma,\delta)$-polycyclic
nature. Furthermore, we classify when two $(\sigma,\delta)$-polycyclic codes
are Hamming isometrical equivalent. By employing Wedderburn polynomials, we
introduce simple-root $(\sigma,\delta)$-polycyclic codes. Subsequently, we
define the $(\sigma, \delta)$-Mattson-Solomon transform for this class of codes
and we address the problem of decomposing these codes by using the properties
of Wedderburn polynomials.
