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.

翻译：本文在特定条件下考虑了具有Moore邻域的二维元胞自动机。具体而言，我们研究了在域$\mathbb{Z}_{p}$上由Moore邻域定义并带有某些混合边界条件的二维线性元胞自动机的特征。此外，我们通过应用旋转操作，探讨了在混合边界条件下二维Moore元胞自动机的规则矩阵。最后，我们给出了二维有限元胞自动机所获得的规则矩阵可逆的条件。