Reconstruction of linear recurrent sequence over prime residue ring from its image. II

Let $v$ be a pseudorandom sequence over $\mathbb Z_p$, $p\ge3$, obtained from primitive sequence $u$ over the ring $\mathbb Z_{p^n}$ by means of some compressing map. We study conditions on the compressing map under which the period of $v$ is less than the period of the initial sequence $u$.