Self-Dual Cyclic Codes over ℤ4[u]/ and Their Applications of ℤ4-Self-Dual Codes Construction
Yun Gao, Jian Gao, Fang‐Wei Fu · IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences · 2018
In this paper, we study self-dual cyclic codes of length n over the ring R=ℤ4[u]/ , where n is an odd positive integer. We define a new Gray map ϕ from R to ℤ42. It is a bijective map and maintains the self-duality. Furthermore, we give the structures of the generators of cyclic codes and self-dual cyclic codes of odd length n over the ring R. As an application, some self-dual codes of length 2n over ℤ4 are obtained.