Let $\underline{ a}$ and $\underline{ b}$ be primitive sequences over $\mathbb{ Z}/(p^e)$ with odd prime $p$ and $e\ge 2$. For certain compressing maps, we consider the distribution properties of compressing sequences of $\underline{ a}$ and $\underline{ b}$, and prove that $\underline{ a}=\underline{ b}$ if the compressing sequences are equal at the times $t$ such that $\alpha(t)=k$, where $\underline{ \alpha}$ is a sequence related to $\underline{ a}$. We also discuss the $s$-uniform distribution property of compressing sequences. For some compressing maps, we have that there exist different primitive sequences such that the compressing sequences are $s$-uniform. We also discuss that compressing sequences can be $s$-uniform for how many elements $s$.
Categories: cs.IT math.IT