设$R=Z_4+u{Z}_4$, $R_n=R[x]/(x^n-(2u-1))$, 其中$u^2=0$, $n=2^e$. 通过对环$R$上码长为$n$的$(2u-1)$-常循环码结构的研究, 得到这些码的生成元, 并对环$R$上码长为$n$的所有$(2u-1)$-常循环码进行分类, 而且研究了该环上$(2u-1)$-常循环码的Hamming距离分布. 最后给出环$R$上码长为$n$的$(2u-1)$-常循环码的对偶码的结构以及环$R$上码长为$n$的自正交与自对偶的$(2u-1)$-常循环码.

Let $R=Z_4+u{Z}_4$, $R_n=R[x]/(x^n-(2u-1))$, where $u^2=0$, $n=2^e$. By studying the structures of $(2u-1)$-constacyclic codes over $R$ of length $n$, we obtain the generators for these codes and classify all $(2u-1)$-constacyclic codes of length $n$ over $R$. Further, we study the Hamming distance distributions of $(2u-1)$-constacyclic codes of length $n$ over $R$. Finally, we give the structures of the duals of $(2u-1)$-constacyclic codes over $R$ of length $n$ and self-orthogonal and self-dual $(2u-1)$-constacyclic codes of length $n$ over $R$.