模奇素数幂本原序列压缩序列的分布性质
Distribution properties of compressing sequences derived from primitive sequences modulo odd prime powers
摘要：
设$\underline{a}$和$\underline{b}$是环$\mathbb{Z}/(p^e)$上的本原序列，其中$p$和$e\ge 2$是奇素数.对于某些压缩映射，我们考虑了$\underline{a}$和$\underline{b}$的压缩序列的分布性质，证明了如果压缩序列在时间$t$上相等，使得$α(t)=k$，则有$\underline{a}=\underline{b}$，其中$\underlineα$是与$\underline{a}$有关的序列.讨论了压缩序列的$s$ -均匀分布性质。对于某些压缩映射，存在不同的本原序列使得压缩序列是$s$ -一致的.我们还讨论了压缩序列对于有多少个元素$s$可以是$s$ -均匀的。
英文摘要：
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 $α(t)=k$, where $\underlineα$ 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 $s$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
