Trace representation and linear complexity of binary sequences derived from Fermat quotients
Trace representation and linear complexity of binary sequences derived from Fermat quotients
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DOI：
10.1007/s11432-014-5092-x
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发表时间：
2013-06
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通讯作者：
Zhixiong Chen
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作者：
Zhixiong Chen
通过确定陪集的所有二元特征序列的定义对，描述了由Fermat商模奇素数导出的两类二元序列（一个是二元阈值序列，另一个是Legendre Fermat商序列）的迹表示.从定义对出发，我们可以得到二元门限序列的线性复杂度的一个较早的结果和勒让德-费马商序列的线性复杂度的一个新的结果。
We describe the trace representations of two families of binary sequences derived from the Fermat quotients modulo an odd primep(one is the binary threshold sequences and the other is the Legendre Fermat quotient sequences) by determining the defining pairs of all binary characteristic sequences of cosets, which coincide with the sets of pre-images modulop2of each fixed value of Fermat quotients. From the defining pairs, we can obtain an earlier result of linear complexity for the binary threshold sequences and a new result of linear complexity for the Legendre Fermat quotient sequences under the assumption of 2p−1≢ 1 modp2.