An algorithm to restore a linear recurring sequence over the ring $R=\mathbf Z_{p^n}$ from a linear complication of its highest coordinate sequence

Let $u$ be a linear recurring sequence of maximal period over the ring $\mathbf Z_{p^n}$ and be a pseudo-random sequence over the field $\mathbf Z_p$ obtained by multiplying the highest coordinate sequence of $u$ by some polynomial. In this paper we analyse possibilities and ways to restore $u$ from a given $v$. A short survey of earlier results is given.