On the linear codes over the ring Z₄+v₁Z₄+...+v_{t}Z₄

Authors : Abdullah DERTLI, Yasemin CENGELLENMIS

Pages : 809-823

Doi:10.31801/cfsuasmas.478655

View : 14 | Download : 13

Publication Date : 2019-02-01

Article Type : Research Paper

Abstract :Some results on linear codes over the ring Z₄+uZ₄+vZ₄,u²=u,v²=v,uv=vu=0 in [6,7] are generalized to the ring D_{t}=Z₄+v₁Z₄+...+v_{t}Z₄,v_{i}²=v_{i},v_{i}v_{j}=v_{j}v_{i}=0 for i≠j,1≤i,j≤t. A Gray map Φ_{t} from D_{t}ⁿ to Z₄^{insert ignore into journalissuearticles values(t+1);n} is defined. The Gray images of the cyclic, constacyclic and quasi-cyclic codes over D_{t} are determined. The cyclic DNA codes over D_{t} are introduced. The binary images of them are determined. The nontrivial automorphism on D_{i} for i=2,3,...,t is given. The skew cyclic, skew constacyclic and skew quasi-cyclic codes over D_{t} are introduced. The Gray images of them are determined. The skew cyclic DNA codes over D_{t} are introduced. Moreover, some properties of MDS codes over D_{t} are discussed.
Keywords : Cyclic codes, skew codes, DNA codes, MDS codes