- Turkish Journal of Mathematics
- Vol: 41 Issue: 5
- Cyclic codes over $\mathbb{Z}_{4}+u\mathbb{Z}_{4}+u^{2}\mathbb{Z}_{4}$
Cyclic codes over $\mathbb{Z}_{4}+u\mathbb{Z}_{4}+u^{2}\mathbb{Z}_{4}$
Authors : Mehmet Özen, Nazmiye Tuğba Özzaim, Nuh Aydin
Pages : 1235-1247
View : 9 | Download : 5
Publication Date : 9999-12-31
Article Type : Makaleler
Abstract :In this paper, we study cyclic codes over the ring $R=\mathbb{Z}_{4}+u\mathbb{Z}_{4}+u^{2}\mathbb{Z}_{4}$,where $u^{3}=0$. We investigate Galois extensions of this ring and the ideal structure of these extensions.The results are then used to obtain facts about cyclic codes over $R$. We also determine the general form of the generator of a cyclic code and find its minimal spanning sets. Finally, we obtain many new linear codes over $\mathbb{Z}_4$ by considering Gray images of cyclic codes over $R$.Keywords : Cyclic codes, Galois extensions, codes over rings, codes over $mathbb{Z}_4$