August  2014, 8(3): 313-322. doi: 10.3934/amc.2014.8.313

Construction of skew cyclic codes over $\mathbb F_q+v\mathbb F_q$

1. 

Department of Mathematics, Yildiz Technical University, 34210, Istanbul, Turkey, Turkey

2. 

Department of Mathematics, Fatih University, 34500, Istanbul

Received  May 2013 Revised  July 2013 Published  August 2014

In this paper skew cyclic codes over the the family of rings $\mathbb{F}_q+v\mathbb{F}_q$ with $v^2=v$ are studied for the first time in its generality. Structural properties of skew cyclic codes over $\mathbb{F}_q+v\mathbb{F}_q$ are investigated through a decomposition theorem. It is shown that skew cyclic codes over this ring are principally generated. The idempotent generators of skew-cyclic codes over $\mathbb{F}_q$ and $\mathbb{F}_q+v\mathbb{F}_q$ have been considered for the first time in literature. Moreover, a BCH type bound is presented for the parameters of these codes.
Citation: Fatmanur Gursoy, Irfan Siap, Bahattin Yildiz. Construction of skew cyclic codes over $\mathbb F_q+v\mathbb F_q$. Advances in Mathematics of Communications, 2014, 8 (3) : 313-322. doi: 10.3934/amc.2014.8.313
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show all references

References:
[1]

IEEE Trans. Inform. Theory, 56 (2010), 2080-2090. doi: 10.1109/TIT.2010.2044062.  Google Scholar

[2]

in Proc. IMECS, Hong Kong, 2010. Google Scholar

[3]

Appl. Algebra Eng. Comm., 18 (2007), 379-389. doi: 10.1007/s00200-007-0043-z.  Google Scholar

[4]

Adv. Math. Commun., 2 (2008), 273-292. doi: 10.3934/amc.2008.2.273.  Google Scholar

[5]

J. Symb. Comput., 44 (2009), 1644-1656. doi: 10.1016/j.jsc.2007.11.008.  Google Scholar

[6]

J. Appl. Math. Inform., 31 (2013), 337-342. doi: 10.14317/jami.2013.337.  Google Scholar

[7]

IEEE Trans. Inform. Theory, 40 (1994), 301-319. doi: 10.1109/18.312154.  Google Scholar

[8]

Adv. Math. Commun., 6 (2012), 29-63. doi: 10.3934/amc.2012.6.39.  Google Scholar

[9]

Marcel Dekker Inc., New York, 1974.  Google Scholar

[10]

Int. J. Inform. Coding Theory, 2 (2011), 10-20. doi: 10.1504/IJICOT.2011.044674.  Google Scholar

[11]

J. Hefei Univ. Technol. Nat. Sci., 34 (2011), 1429-1432.  Google Scholar

[12]

IEEE Trans. Inform. Theory, 56 (2010), 1680-1684. doi: 10.1109/TIT.2010.2040896.  Google Scholar

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