关于由Euler导数导出的伪随机序列的$k$ -错线性复杂度
On $k$-error linear complexity of pseudorandom binary sequences derived from Euler quotients
摘要：
本文研究了周期为$p^{\mathfrak{r}}$的伪随机二进制序列的$k$ -错误线性复杂度，该序列是由模$p^{\mathfrak{r}-1}$的欧拉导数导出的，是$\mathfrak{r}\geq 2$的奇素数$p$的幂.当$\mathfrak{r}=2$，这只是情况下的多项式幂次（包括费马幂次）模$p$，这已经研究了在早期的工作陈，牛和吴。在这项工作中，我们建立了一个递归关系的$k$ -错误的线性复杂度的序列的情况下，$\mathfrak{r}\geq 3$。我们还陈述了$\mathfrak{r}=3$的情况下的$k$ -错误线性复杂度的精确值。从结果中，我们可以发现对于$k<p^{\mathfrak{r}-2}(p-1)^2/2$，（周期为$p^{\mathfrak{r}}$的）序列的$k$ -错误线性复杂度没有显著降低。
英文摘要：
We investigate the $k$-error linear complexity of pseudorandom binary sequences of period $p^{\mathfrak{r}}$ derived from the Euler quotients modulo $p^{\mathfrak{r}-1}$, a power of an odd prime $p$ for $\mathfrak{r}\geq 2$. When $\mathfrak{r}=2$, this is just the case of polynomial quotients (including Fermat quotients) modulo $p$, which has been studied in an earlier work of Chen, Niu and Wu. In this work, we establish a recursive relation on the $k$-error linear complexity of the sequences for the case of $\mathfrak{r}\geq 3$. We also state the exact values of the $k$-error linear complexity for the case of $\mathfrak{r}=3$. From the results, we can find that the $k$-error linear complexity of the sequences (of period $p^{\mathfrak{r}}$) does not decrease dramatically for $k<p^{\mathfrak{r}-2}(p-1)^2/2$.
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。
