Self-Dual Cyclic Codes over ℤ₄[u]/<u²-1> and Their Applications of ℤ₄-Self-Dual Codes Construction

Abstract

In this paper, we study self-dual cyclic codes of length n over the ring R=ℤ₄[u]/<u²-1>, 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.