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Skew-cyclic and skew-quasi-cyclic codes over a general infinite family of rings | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 16 تیر 1404 | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2025.29232.1901 | ||
| نویسندگان | ||
| Djoko Suprijanto* 1، 2؛ Irwansyah Irwansyah3 | ||
| 1Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jl. Ganesha 10, Bandung, 40132, Indonesia | ||
| 2Center for Research Collaboration on Graph Theory and Combinatorics, Indonesia | ||
| 3Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Mataram, Mataram, Indonesia | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Commutative Frobenius ring؛ quasi-cyclic code؛ skew-cyclic code؛ skew-quasi-cyclic code؛ optimal codes over $\ZZ_4.$ | ||
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آمار تعداد مشاهده مقاله: 9 |
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