A study on structure of codes over $\mathbb Z_4+u\mathbb Z_4+v\mathbb Z_4 $

Document Type : Original paper

Author

Department of Mathematics, Presidency University, Bangalore, Karnataka, India

Abstract

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)].

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References

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Communications in Combinatorics and Optimization
Volume 9, Issue 3
September 2024
Pages 567-578

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