Year 2019, Volume 6 , Issue 3, Pages 163 - 172 2019-09-13

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

Tushar BAG [1] , Habibul ISLAM [2] , Om PRAKASH [3] , Ashish K. UPADHYAY [4]


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 $R$.
Constacyclic codes, Skew constacyclic codes, Gray map, Quasi-cyclic codes
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Primary Language en
Subjects Engineering
Journal Section Articles
Authors

Orcid: 0000-0002-7613-8351
Author: Tushar BAG

Orcid: 0000-0002-2196-1586
Author: Habibul ISLAM

Orcid: 0000-0002-6512-4229
Author: Om PRAKASH (Primary Author)

Orcid: 0000-0001-6307-6799
Author: Ashish K. UPADHYAY

Dates

Publication Date : September 13, 2019

Bibtex @research article { jacodesmath617244, journal = {Journal of Algebra Combinatorics Discrete Structures and Applications}, issn = {}, eissn = {2148-838X}, address = {}, publisher = {Yildiz Technical University}, year = {2019}, volume = {6}, pages = {163 - 172}, doi = {10.13069/jacodesmath.617244}, title = {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\$}, key = {cite}, author = {Bag, Tushar and Islam, Habibul and Prakash, Om and Upadhyay, Ashish K.} }
APA Bag, T , Islam, H , Prakash, O , Upadhyay, A . (2019). 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 , 6 (3) , 163-172 . DOI: 10.13069/jacodesmath.617244
MLA Bag, T , Islam, H , Prakash, O , Upadhyay, A . "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 6 (2019 ): 163-172 <https://dergipark.org.tr/en/pub/jacodesmath/issue/48724/617244>
Chicago Bag, T , Islam, H , Prakash, O , Upadhyay, A . "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 6 (2019 ): 163-172
RIS TY - JOUR T1 - A note on constacyclic and skew constacyclic codes over the ring $\mathbb{Z}_{p} [u,v]/\langle u^2-u,v^2-v,uv-vu\rangle$ AU - Tushar Bag , Habibul Islam , Om Prakash , Ashish K. Upadhyay Y1 - 2019 PY - 2019 N1 - doi: 10.13069/jacodesmath.617244 DO - 10.13069/jacodesmath.617244 T2 - Journal of Algebra Combinatorics Discrete Structures and Applications JF - Journal JO - JOR SP - 163 EP - 172 VL - 6 IS - 3 SN - -2148-838X M3 - doi: 10.13069/jacodesmath.617244 UR - https://doi.org/10.13069/jacodesmath.617244 Y2 - 2019 ER -
EndNote %0 Journal of Algebra Combinatorics Discrete Structures and Applications A note on constacyclic and skew constacyclic codes over the ring $\mathbb{Z}_{p} [u,v]/\langle u^2-u,v^2-v,uv-vu\rangle$ %A Tushar Bag , Habibul Islam , Om Prakash , Ashish K. Upadhyay %T A note on constacyclic and skew constacyclic codes over the ring $\mathbb{Z}_{p} [u,v]/\langle u^2-u,v^2-v,uv-vu\rangle$ %D 2019 %J Journal of Algebra Combinatorics Discrete Structures and Applications %P -2148-838X %V 6 %N 3 %R doi: 10.13069/jacodesmath.617244 %U 10.13069/jacodesmath.617244
ISNAD Bag, Tushar , Islam, Habibul , Prakash, Om , Upadhyay, Ashish K. . "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 6 / 3 (September 2019): 163-172 . https://doi.org/10.13069/jacodesmath.617244
AMA Bag T , Islam H , Prakash O , Upadhyay A . 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. 2019; 6(3): 163-172.
Vancouver Bag T , Islam H , Prakash O , Upadhyay A . 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. 2019; 6(3): 163-172.