Skew cyclic codes over ℤ_4+vℤ_4 with derivation
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In this work, we study a class of skew cyclic codes over the ring R:=ℤ_4+vℤ_4, where v^2=v, with an automorphism θ and a derivation Δ_θ, namely codes as modules over a skew polynomial ring R[x;θ,Δ_θ], whose multiplication is defined using an automorphism θ and a derivation Δ_θ. We investigate the structures of a skew polynomial ring R[x;θ,Δ_θ]. We define Δ_θ-cyclic codes as a generalization of the notion of cyclic codes. The properties of Δ_θ-cyclic codes as well as dual Δ_θ-cyclic codes are derived. Some new codes over ℤ_4 with good parameters are obtained via a Gray map as well as residue and torsion codes of these codes.
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