2D Moore CA with new boundary conditions and its reversibility

In this paper, under certain conditions we consider two-dimensional cellular automata with the Moore neighborhood. Namely, the characterization of 2D linear cellular automata defined by the Moore neighborhood with some mixed boundary conditions over the field $\mathbb{Z}_{p}$ is studied. Furthermore, we investigate the rule matrices of 2D Moore CA under some mixed boundary conditions by applying rotation. Finally, we give the conditions under which the obtained rule matrices for 2D finite CAs are reversible.