In this paper, we first consider the iterated skew polynomial ring $\mathscr{R}[z_1;\tau_1,\delta_{\tau_1}]$\\$[z_2;\tau_2,\delta_{\tau_2}]$, where $\mathscr{R}$ is a finite ring with unity. Then we use this structure for the construction of skew generalized polycyclic codes over the ring $\mathscr{R}$ and finite field $\mathbb{F}_q$, where $q=p^m$ for some positive integer $m$. Further, we derive the structure of the generator and parity check matrices for skew generalized polycyclic codes. Furthermore, we improve the Bose-Chaudhuri-Hocquenghem (BCH) lower bound for a minimum distance of skew generalized polycyclic codes with non-zero derivations over a finite field. Moreover, we find a sufficient condition for a code to be a maximum-distance-separable (MDS) code. In addition, we provide examples of MDS codes to show the importance of our results. A comparative summary of our work with other linear codes is also discussed.

翻译：本文首先考虑迭代斜多项式环 $\mathscr{R}[z_1;\tau_1,\delta_{\tau_1}]$\\$[z_2;\tau_2,\delta_{\tau_2}]$，其中 $\mathscr{R}$ 是一个具有单位元的有限环。然后，我们利用该结构在环 $\mathscr{R}$ 和有限域 $\mathbb{F}_q$（其中 $q=p^m$，$m$ 为正整数）上构造斜广义多循环码。进一步，我们推导了斜广义多循环码的生成矩阵和校验矩阵的结构。此外，我们改进了有限域上带非零导子的斜广义多循环码最小距离的 Bose-Chaudhuri-Hocquenghem (BCH) 下界。而且，我们找到了一个码成为最大距离可分 (MDS) 码的充分条件。另外，我们提供了 MDS 码的示例以展示我们结果的重要性。本文还讨论了我们的工作与其他线性码的比较性总结。