A note on constacyclic and skew constacyclic codes over the ring $\mathbb{Z}_{p} [u,v]/\langle u^2-u,v^2-v,uv-vu\rangle$
DOI:
https://doi.org/10.13069/jacodesmath.617244Keywords:
Constacyclic codes, Skew constacyclic codes, Gray map, Quasi-cyclic codesAbstract
For odd prime $p$, this paper studies $(1+(p-2)u)$-constacyclic codes over the ring $R= \mathbb{Z}_{p} [u,v]/\langle u^2-u,v^2-v,uv-vu\rangle$. We show that the Gray images of $(1+(p-2)u)$-constacyclic codes over $R$ are cyclic and permutation equivalent to a quasi cyclic code over $\mathbb{Z}_{p}$. We derive the generators for $(1+(p-2)u)$-constacyclic and principally generated $(1+(p-2)u)$-constacyclic codes over $R$. Among others, we extend our results for skew $(1+(p-2)u)$-constacyclic codes over $R$ and exhibit the relation between skew $(1+(p-2)u)$-constacyclic codes with the other linear codes. Finally, as an application of our study, we compute several non trivial linear codes by using the Gray images of $(1+(p-2)u)$-constacyclic codes over this ring $R$.
Received: 20 October 2018 Accepted: 21 August 2019Downloads
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