Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 Articles in Press 2025 07 07 Skew-cyclic and skew-quasi-cyclic codes over a general infinite family of rings 14981 10.22049/cco.2025.29232.1901 EN Djoko Suprijanto Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jl. Ganesha 10, Bandung, 40132, Indonesia Center for Research Collaboration on Graph Theory and Combinatorics, Indonesia Irwansyah Irwansyah Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Mataram, Mataram, Indonesia Journal Article 2023 11 30 We study structural properties of cyclic codes, and their generalization, over a general infinite family of rings, namely the ring $\mathcal{R}_k$ defined by $R[v_1,v_2,\ldots,v_k]$ with conditions $v_i^2=v_i,$ for $i \in [1,k]_\ZZ,$ where $R$ is any finite commutative Frobenius ring. We derived necessary and sufficient condition for the codes to be cyclic, quasi-cyclic, skew-cyclic as well as to be quasi-skew-cyclic. As an application, we constructed optimal linear codes over $\ZZ_4$ as a Gray images of our codes. https://comb-opt.azaruniv.ac.ir/article_14981_3a086edb0d197b532516b291ba44be7f.pdf