## Tbilisi Mathematical Journal

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

#### 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

#### 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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