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A study on structure of codes over $\mathbb Z_4+u\mathbb Z_4+v\mathbb Z_4 $ | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 13، دوره 9، شماره 3، آذر 2024، صفحه 567-578 اصل مقاله (390.49 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2023.28011.1503 | ||
| نویسنده | ||
| Gowdhaman Karthick* | ||
| Department of Mathematics, Presidency University, Bangalore, Karnataka, India | ||
| چکیده | ||
| We study $(1+2u+2v)$-constacyclic code over a semi-local ring $S=\mathbb Z_4+u\mathbb Z_4+v\mathbb Z_4$ with the condition $u^2=3u,v^2=3v$, and $uv=vu=0$, we show that $(1+2u+2v)$-constacyclic code over $S$ is equivalent to quasi-cyclic code over $\mathbb{Z}_4$ by using two new Gray maps from $S$ to $\mathbb{Z}_4.$ Also, for odd length $n$ we have defined a generating set for constacyclic codes over $S.$ Finally, we obtained some examples which are new to the data base [Database of $\mathbb{Z}_4$ codes [online]}, http://$\mathbb{Z}_4$ Codes.info(Accessed March 2, 2020)]. | ||
| کلیدواژهها | ||
| Cyclic codes؛ Generating set؛ Gray maps | ||
| مراجع | ||
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