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Skew cyclic codes over $\mathbb{Z}_4+v\mathbb{Z}_4$ with derivation: structural properties and computational results | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 24 دی 1402 اصل مقاله (480.85 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2024.28837.1744 | ||
| نویسندگان | ||
| Djoko Suprijanto* 1؛ Hopein Christofen Tang2 | ||
| 1Department of Mathematics, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung, INDONESiA | ||
| 2School of Mathematics and Statistics, UNSW, Sydney, Australia | ||
| چکیده | ||
| In this work, we study a class of skew cyclic codes over the ring $R:=\mathbb{Z}_4+v\mathbb{Z}_4,$ where $v^2=v,$ with an automorphism $\theta$ and a derivation $\Delta_\theta,$ namely codes as modules over a skew polynomial ring $R[x;\theta,\Delta_{\theta}],$ whose multiplication is defined using an automorphism $\theta$ and a derivation $\Delta_{\theta}.$ We investigate the structures of a skew polynomial ring $R[x;\theta,\Delta_{\theta}].$ We define $\Delta_{\theta}$-cyclic codes as a generalization of the notion of cyclic codes. The properties of $\Delta_{\theta}$-cyclic codes as well as dual $\Delta_{\theta}$-cyclic codes are derived. As an application, some new linear codes over $\mathbb{Z}_4$ with good parameters are obtained by Plotkin sum construction, also via a Gray map as well as residue and torsion codes of these codes. | ||
| کلیدواژه‌ها | ||
| Cyclic codes؛ quasi-cyclic codes؛ skew polynomial ring؛ skew cyclic codes؛ derivation | ||
| مراجع | ||
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