Trace representation and linear complexity of binary sequences derived from Fermat quotients

We describe the trace representations of two families of binary sequences derived from the Fermat quotients modulo an odd prime p （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 o...

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Bibliographic Details
Published in:Science China. Information sciences 2014-11, Vol.57 (11), p.116-125
Main Author: Chen, ZhiXiong
Format: Article
Language:English
Subjects:
China
Complexity
Computer Science
Information Systems and Communication Service
Quotients
Representations
Research Paper
Thresholds
二进制序列
商数
奇素数
特征序列
线性复杂性
费尔马
费马
迹表示
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Summary:We describe the trace representations of two families of binary sequences derived from the Fermat quotients modulo an odd prime p （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 modulo p2 of 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 mod p2.
ISSN:1674-733X
1869-1919
DOI:10.1007/s11432-014-5092-x