Construction of skew cyclic and skew constacyclic codes over Fq+uFq+vFq

In this paper, skew cyclic and skew constacyclic codes over finite non-chain ring R = F_q+uF_q+vF_q, where q= p^m, p is an odd prime and u^{2}=u, v^{2}=v, uv=vu=0 are studied. We show that Gray image of a skew cyclic code of length n over R is a skew quasi-cyclic code of length 3n over F_q of index 3. Structural properties of skew cyclic and skew constacyclic over R are obtained. Further, generating polynomials and idempotent generators of both skew cyclic and skew constacyclic codes over R are determined by decomposition method.

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

[2]  Ayman Badawi,et al.  Quantum Codes Over F 2 + uF 2 + vF 2 , 2015 .

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

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

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

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