Skew Cyclic codes over $\F_q+u\F_q+v\F_q+uv\F_q$

In this paper, we study skew cyclic codes over the ring $R=\F_q+u\F_q+v\F_q+uv\F_q$, where $u^{2}=u,v^{2}=v,uv=vu$, $q=p^{m}$ and $p$ is an odd prime. We investigate the structural properties of skew cyclic codes over $R$ through a decomposition theorem. Furthermore, we give a formula for the number of skew cyclic codes of length $n$ over $R.$

[1]  Felix Ulmer,et al.  Skew-cyclic codes , 2006, Applicable Algebra in Engineering, Communication and Computing.

[2]  N. J. A. Sloane,et al.  The Z4-linearity of Kerdock, Preparata, Goethals, and related codes , 1994, IEEE Trans. Inf. Theory.

[3]  Frank W. Anderson,et al.  Rings and Categories of Modules , 1974 .

[4]  Taher Abualrub,et al.  Skew cyclic codes of arbitrary length , 2011, Int. J. Inf. Coding Theory.

[5]  Jian Gao,et al.  Skew Generalized Quasi-Cyclic Codes over Finite Fields , 2013, ArXiv.

[6]  Felix Ulmer,et al.  Coding with skew polynomial rings , 2009, J. Symb. Comput..

[7]  Patanee Udomkavanich,et al.  Skew constacyclic codes over finite chain rings , 2010, Adv. Math. Commun..

[8]  Jian Gao.  SKEW CYCLIC CODES OVER Fp+ vFp , 2013 .

[9]  Fernando Hernando,et al.  Sixteen New Linear Codes With Plotkin Sum , 2008, ArXiv.

[10]  Bahattin Yildiz,et al.  Construction of skew cyclic codes over 픽q+v픽q , 2014, Adv. Math. Commun..

[11]  Patrick Solé,et al.  Skew constacyclic codes over Galois rings , 2008, Adv. Math. Commun..