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^{(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.
Birincil Dil | İngilizce |
---|---|
Bölüm | Makaleler |
Yazarlar | |
Yayımlanma Tarihi | 1 Şubat 2019 |
Gönderilme Tarihi | 27 Ağustos 2016 |
Kabul Tarihi | 30 Aralık 2017 |
Yayımlandığı Sayı | Yıl 2019 Cilt: 68 Sayı: 1 |
Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.
This work is licensed under a Creative Commons Attribution 4.0 International License.