On Skew Polycyclic Codes over $\mathbb{Z}_4[u]/\langle u^2-2\rangle$

Abstract:

      In this paper, we investigate some classes of skew polycyclic codes and polycyclic codes over $R=\mathbb{Z}_4[u]/\langle u^2-2\rangle$. We first obtain the generator polynomials of all $(1,2u)$-polycyclic codes over $R$. Then, by defining some Gray maps, we show that the images of (skew) $(1,2u)$-polycyclic codes over $R$ are cyclic or quasi-cyclic with index 2 over $\mathbb{Z}_4$. Finally, an example of some $(1,2u)$-polycyclic codes over $R$ is given to exhibit the main results of the paper.