New results on periodic sequences with large k-error linear complexity

Authors:
Honggang Hu;Guang Gong;Dengguo Feng
Affiliations:
Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON, Canada and State Key Laboratory of Information Security, Institute of Software, Chinese Academy of Sciences ...;Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON, Canada;State Key Laboratory of Information Security, Institute of Software, Chinese Academy of Sciences, Beijing, China
Venue:
IEEE Transactions on Information Theory
Year:
2009

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Abstract

Niederreiter showed that there is a class of periodic sequences which possess large linear complexity and large k-error linear complexity simultaneously. This result disproved the conjecture that there exists a trade-off between the linear complexity and the k-error linear complexity of a periodic sequence by Ding et al. By considering the orders of the divisors of xN - 1 over Fq, we obtain three main results which hold for much larger k than those of Niederreiter et al.: a) sequences with maximal linear complexity and almost maximal k-error linear complexity with general periods; b) sequences with maximal linear complexity and maximal k-error linear complexity with special periods; c) sequences with maximal linear complexity and almost maximal k-error linear complexity in the asymptotic case with composite periods. Besides, we also construct some periodic sequences with lowcorrelation and large k-error linear complexity.