A note on constacyclic and skew constacyclic codes over the ring $\mathbb{Z}_{p} [u,v]/\langle u^2-u,v^2-v,uv-vu\rangle$

Journal of Algebra Combinatorics Discrete Structures and Applications

article

Tushar Bag¹  Habibul Islam¹  Om Prakash¹  Ashish K. Upadhyay¹ 

[1] Department of Mathematics, Indian Institute of Technology Patna

关键词: Constacyclic codes;    Skew constacyclic codes;    Gray map;    Quasi-cyclic codes;   

DOI  :  10.13069/jacodesmath.617244

学科分类：社会科学、人文和艺术（综合）

来源: Yildiz Technical University

【 摘 要 】

For odd prime p, this paper studies (1 + (p−2)u)-constacyclic codes over the ring R = Zp[u, v]/hu2 −u, v2 − v, uv − vui. We show that the Gray images of (1 + (p − 2)u)-constacyclic codes over Rare cyclic and permutation equivalent to a quasi cyclic code over Zp. We derive the generatorsfor (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 exhibitthe relation between skew (1 + (p − 2)u)-constacyclic codes with the other linear codes. Finally, asan 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.

【 授权许可】

CC BY