Linear complexity of Legendre-polynomial quotients

Zhixiong Chen
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引用次数: 1

Abstract

We continue to investigate binary sequence $(f_u)$ over $\{0,1\}$ defined by $(-1)^{f_u}=\left(\frac{(u^w-u^{wp})/p}{p}\right)$ for integers $u\ge 0$, where $\left(\frac{\cdot}{p}\right)$ is the Legendre symbol and we restrict $\left(\frac{0}{p}\right)=1$. In an earlier work, the linear complexity of $(f_u)$ was determined for $w=p-1$ under the assumption of $2^{p-1}\not\equiv 1 \pmod {p^2}$. In this work, we give possible values on the linear complexity of $(f_u)$ for all $1\le w
legende -多项式商的线性复杂度
我们继续研究由$(-1)^{f_u}=\left(\frac{(u^w-u^{wp})/p}{p}\right)$为整数$u\ge 0$定义的$\{0,1\}$上的二进制序列$(f_u)$,其中$\left(\frac{\cdot}{p}\right)$是Legendre符号,并且我们限制$\left(\frac{0}{p}\right)=1$。在较早的工作中,在$2^{p-1}\not\equiv 1 \pmod {p^2}$的假设下,确定了$w=p-1$的线性复杂度$(f_u)$。在这项工作中,我们给出了在相同条件下所有$1\le w
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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