Skew polycyclic codes over 𝔽q + u𝔽q + v𝔽q + uv𝔽q

In this paper, we study skew polycyclic codes over the ring [Formula: see text] where [Formula: see text] and [Formula: see text] where [Formula: see text] is an odd prime. We investigate the structural properties of skew polycyclic codes over [Formula: see text] through a decomposition theorem. Furthermore, we examine the dual codes of skew polycyclic codes over R, providing necessary and sufficient conditions for a code to be self-dual. We investigate the Gray images of skew polycyclic codes over R, focusing on codes with good parameters. We discuss skew polycyclic codes over the ring [Formula: see text] with even characteristic and provide several illustrative examples to support the theoretical results.