Linear complexity of binary sequences derived from polynomial quotients

Authors:
Zhixiong Chen;Domingo Gómez-Pérez
Affiliations:
Department of Mathematics, Putian University, Putian, Fujian, P.R. China,State Key Laboratory of Information Security, Institute of Software, Chinese Academy of Sciences, Beijing, P.R. China;University of Cantabria, Santander, Spain
Venue:
SETA'12 Proceedings of the 7th international conference on Sequences and Their Applications
Year:
2012

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Abstract

We determine the linear complexity of p2-periodic binary threshold sequences derived from polynomial quotient, which is defined by the function $(u^w-u^{wp})/p \pmod p$. When w=(p−1)/2 and $2^{p-1}\not\equiv 1 \pmod{p^2}$, we show that the linear complexity is equal to one of the following values $\left\{p^2-1,\ p^2-p,\ (p^2+p)/2+1,\ (p^2-p)/2\right \}$, depending whether $p\equiv 1,\ -1,\ 3,\ -3\pmod 8$. But it seems that the method can't be applied to the case of general w.