A note on constacyclic and skew constacyclic codes over the ring Zp[u, v]/hu 2 − u, v2 − v, uv − vui

Year 2019, Volume: 6 Issue: 3, 163 - 172, 13.09.2019

Tushar Bag Habibul Islam , Om Prakash , Ashish K. Upadhyay

https://doi.org/10.13069/jacodesmath.617244

Cited By: 7

Abstract

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 $R$.

Keywords

Constacyclic codes, Skew constacyclic codes, Gray map, Quasi-cyclic codes

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