Tbilisi Mathematical Journal

On skew cyclic codes over $F_{q}+vF_{q}+v^2F_{q}$

Mohammad Ashraf and Ghulam Mohammad

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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.

Note

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

Article information

Source
Tbilisi Math. J., Volume 11, Issue 2 (2018), 35-45.

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

Permanent link to this document
https://projecteuclid.org/euclid.tbilisi/1529460020

Digital Object Identifier
doi:10.32513/tbilisi/1529460020

Mathematical Reviews number (MathSciNet)
MR3954181

Zentralblatt MATH identifier
06984247

Subjects
Primary: 94B05: Linear codes, general
Secondary: 94B15: Cyclic codes

Keywords
dual codes quasi cyclic codes skew polynomial rings skew cyclic codes idempotent generators

Citation

Ashraf, Mohammad; Mohammad, Ghulam. On skew cyclic codes over $F_{q}+vF_{q}+v^2F_{q}$. Tbilisi Math. J. 11 (2018), no. 2, 35--45. doi:10.32513/tbilisi/1529460020. https://projecteuclid.org/euclid.tbilisi/1529460020


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