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Cyclic codes over non-Frobenius ring $\mathbb{Z}_4+u\mathbb{Z}_4+v\mathbb{Z}_4$ | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 14 شهریور 1405 اصل مقاله (514.78 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2026.30614.2554 | ||
| نویسندگان | ||
| Zahra Goodarzi* 1؛ Mohammadreza Alimoradi* 1؛ Nuh Aydin2 | ||
| 1Faculty of Mathematical Sciences and Statistics, Malayer University, Malayer, Iran | ||
| 2Department of Mathematics and Statistics, Kenyon College, 43022 Gambier, OH, USA | ||
| چکیده | ||
| In this study, cyclic codes of odd length over the ring $R=\mathbb Z_4+u\mathbb Z_4+v\mathbb Z_4$ are investigated. The structure of cyclic codes over this ring is characterized using the work Samie and Alimoradi (Comp. Appl. Math. 2018). The ranks and duals of such codes are determined. It is also shown that the equality $|C||C^\bot|=|R|^n$ holds for a cyclic code $C$ of length $n$ over this ring if and only if $C$ is a cyclic code over the Frobenius subring $\mathbb{Z}_4+u\mathbb{Z}_4$ of the non-Frobenius ring $R.$ Moreover, we correct a false claim about this ring that appeared in the literature. Finally, several new linear codes over $\mathbb{Z}_4$ are obtained from cyclic codes over $R$ via a Gray map. | ||
| کلیدواژه‌ها | ||
| Cyclic codes؛ Self-dual codes؛ Frobenius ring؛ Gray map | ||
| مراجع | ||
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