Azarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21289320240901A study on structure of codes over $\mathbb Z_4+u\mathbb Z_4+v\mathbb Z_4 $5675781454810.22049/cco.2023.28011.1503ENGowdhamanKarthickDepartment of Mathematics, Presidency University, Bangalore, Karnataka, IndiaJournal Article20220919We 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)].http://comb-opt.azaruniv.ac.ir/article_14548_e6fe5c8749c957f757c7ff47ae8f2470.pdf