Translator Disclaimer
June 2018 On skew cyclic codes over $F_{q}+vF_{q}+v^2F_{q}$
Mohammad Ashraf, Ghulam Mohammad
Tbilisi Math. J. 11(2): 35-45 (June 2018). DOI: 10.32513/tbilisi/1529460020

Abstract

In the present paper, we study skew cyclic codes over the ring $F_{q}+vF_{q}+v^2F_{q}$, where $v^3=v,~q=p^m$ and $p$ is an odd prime. The structural properties of skew cyclic codes over $F_{q}+vF_{q}+v^2F_{q}$ have been studied by using decomposition method. By defining a Gray map from $F_{q}+vF_{q}+v^2F_{q}$ to $F_{q}^3$, it has been proved that the Gray image of a skew cyclic code of length $n$ over $F_{q}+vF_{q}+v^2F_{q}$ is a skew $3$-quasi cyclic code of length $3n$ over $F_{q}$. Further, it is shown that the skew cyclic codes over $F_{q}+vF_{q}+v^2F_{q}$ are principally generated. Finally, the idempotent generators of skew cyclic codes over $F_{q}+vF_{q}+v^2F_{q}$ have also been studied.

Acknowledgment

The authors are thankful to the anonymous referees for their careful reading of the paper and valuable comments.

Citation

Download Citation

Mohammad Ashraf. Ghulam Mohammad. "On skew cyclic codes over $F_{q}+vF_{q}+v^2F_{q}$." Tbilisi Math. J. 11 (2) 35 - 45, June 2018. https://doi.org/10.32513/tbilisi/1529460020

Information

Received: 16 June 2017; Accepted: 25 January 2018; Published: June 2018
First available in Project Euclid: 20 June 2018

MathSciNet: MR3954181
zbMATH: 06984247
Digital Object Identifier: 10.32513/tbilisi/1529460020

Subjects:
Primary: 94B05
Secondary: 94B15

Rights: Copyright © 2018 Tbilisi Centre for Mathematical Sciences

JOURNAL ARTICLE
11 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.11 • No. 2 • June 2018
Back to Top