On the linear complexity of binary threshold sequences derived from Fermat quotients
On the linear complexity of binary threshold sequences derived from Fermat quotients
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DOI：
10.1007/s10623-012-9608-3
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发表时间：
2013-06
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通讯作者：
Zhixiong Chen;Xiaoni Du
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文献类型：
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作者：
Zhixiong Chen;Xiaoni Du
本文研究了一类由费马系数模奇素数p导出的p ~ 2周期二元门限序列的线性复杂度，其中p满足。线性复杂度等于sp2 − porp 2 − 1，取决于或3（mod 4）。我们的研究扩展了以前的工作相应的二进制阈值序列的线性复杂度的结果时，2是一个原根modulop 2。此外，我们还给出了它们的素数线性复杂度的一个部分结果。然而，这种所谓的Wieferich素数非常罕见。
We determine the linear complexity of a family ofp2-periodic binary threshold sequences derived from Fermat quotients modulo an odd primep, wherepsatisfies. The linear complexity equalsp2−porp2− 1, depending whetheror 3 (mod 4). Our research extends the results from previous work on the linear complexity of the corresponding binary threshold sequences when 2 is a primitive root modulop2. Moreover, we present a partial result on their linear complexities for primespwith. However such so called Wieferich primes are very rare.