A note on constacyclic codes over the ring z_3[u, v]/
Abstract
In this paper, we study λ-constacyclic codes over the ring R = Z3[u, v]/<u2 − u, v2, uv, vu> for λ = (1 + u),(2 + 2u) and 2. We introduce a Gray map from R to Z33 and show that the Gray image of a cyclic code is a quasi-cyclic code of index 3. It is proved that the Gray image of λ-constacyclic code over R is permutation equivalent to either quasi-cyclic or quasi-twisted code according to the value of λ. Moreover, we determine the structure of (1+u)-constacyclic codes for an odd length n over R and give some suitable examples.
Copyright © 2021 St. Timothy Kom, O. Ratnabala Devi, Th. Rojita Chanu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
S. T. Kom, O. R. Devi, T. R. Chanu, A note on constacyclic codes over the ring z_3[u, v]/, J. Math. Comput. Sci. 11 (2021), 1437–1454. https://doi.org/10.28919/jmcs/5206
BibTeX
@article{Kom2021,
author = {Kom, St. Timothy and Devi, O. Ratnabala and Chanu, Th. Rojita},
title = {A note on constacyclic codes over the ring z_3[u, v]/},
journal = {J. Math. Comput. Sci.},
volume = {11},
year = {2021},
pages = {1437--1454},
doi = {10.28919/jmcs/5206}
}