  Let $p\geq3$ be a prime and $e\geq2$ an integer. Let $\sigma(x)$ be a
primitive polynomial of degree $n$ over $Z/p^eZ$ and $G'(\sigma(x),p^e)$ the
set of primitive linear recurring sequences generated by $\sigma(x)$. A
compressing map $\varphi$ on $Z/p^eZ$ naturally induces a map $\hat{\varphi}$
on $G'(\sigma(x),p^e)$. For a subset $D$ of the image of
$\varphi$,$\hat{\varphi}$ is called to be injective w.r.t. $D$-uniformity if
the distribution of elements of $D$ in the compressed sequence implies all
information of the original primitive sequence. In this correspondence, for at
least $1-2(p-1)/(p^n-1)$ of primitive polynomials of degree $n$, a clear
criterion on $\varphi$ is obtained to decide whether $\hat{\varphi}$ is
injective w.r.t. $D$-uniformity, and the majority of maps on $Z/p^eZ$ induce
injective maps on $G'(\sigma(x),p^e)$. Furthermore, a sufficient condition on
$\varphi$ is given to ensure injectivity of $\hat{\varphi}$ w.r.t.
$D$-uniformity. It follows from the sufficient condition that if $\sigma(x)$ is
strongly primitive and the compressing map $\varphi(x)=f(x_{e-1})$, where
$f(x_{e-1})$ is a permutation polynomial over $\mathbb{F}_{p}$, then
$\hat{\varphi}$ is injective w.r.t. $D$-uniformity for $\emptyset\neq
D\subset\mathbb{F}_{p}$. Moreover, we give three specific families of
compressing maps which induce injective maps on $G'(\sigma(x),p^e)$.
