设~$p$~为素数,文章研究了环~${\mathbb{Z}}_{p^2}$ 上长为~$n$ 的循环自正交码的结构, 其中~$n$ 与~$p$ 互素. 利用~${\mathbb{Z}}_{p^2}$ 上长为~$n$ 的循环码 的生成多项式, 得到了~${\mathbb{Z}}_{p^2}$ 上长为~$n$ 的 循环自正交码存在的充要条件, 由此给出了~${\mathbb{Z}}_{p^2}$ 上长为~$n$ 的循环自正交码的构造方法, 并且确定了这类码的数目.

In this paper, the structure of cyclic self-orthogonal codes over the ring ${\mathbb{Z}}_{p^2}$ of length $n$ is studied, where $n$ and $p$ are relatively coprime and $p$ is a prime. By using the generator polynomial of cyclic codes over ${\mathbb{Z}}_{p^2}$ of length $n$, a sufficient and necessary condition for the existence of cyclic self-orthogonal codes over ${\mathbb{Z}}_{p^2}$ of length $n$ is obtained. Further, a method of constructing cyclic self-orthogonal codes over ${\mathbb{Z}}_{p^2}$ of length $n$ is given and the number of such codes is determined.