On Constacyclic Codes Over $\mathbb{Z}_4[v]/\langle v^2-v \rangle$ and Their Gray Images
Hai Quang Dinh, Abhay Kumar Singh, Narendra Kumar, Songsak Sriboonchitta · IEEE Communications Letters · 2018
In this letter, we discuss the construction of all constacyclic codes over$R = \mathbb {Z}_{4}[v]/\langle v^{2}-v \rangle $. Some significant properties of linear codes over$R$have been explored. The self-dual constacyclic codes for odd length over$R$are determined. Several examples of$(1 + {2}v)$- constacyclic codes and$(3 + {2}v)$-constacyclic codes over$R$, whose$\mathbb {Z}_{4}$-images are new$\mathbb {Z}_{4}$-linear codes with better parameters, are provided.