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Characterization of the third descent points for the k-error linear complexity of 2n-periodic binary sequences

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Authors
Zhou, J.
Liu, Wan-Quan
Wang, X.
Date
2016
Type
Book Chapter

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Zhou, J. and Liu, W. and Wang, X. 2016. Characterization of the third descent points for the k-error linear complexity of 2n-periodic binary sequences, in Proceedings of the International Conference on Information and Communications Security (ICICS), Dec 9-11 2015, pp. 169-183. Bejing, China: Springer.
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Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
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Department of Computing
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Abstract

In this paper, a structural approach for determining CELCS (critical error linear complexity spectrum) for the k-error linear complexity distribution of 2n-periodic binary sequences is developed via the sieve method and Games-Chan algorithm. Accordingly, the third descent point (critical point) distribution of the k-error linear complexity for 2n- periodic binary sequences is characterized. As a consequence, we derive the complete counting functions on the 5-error linear complexity of 2n- periodic binary sequences when it is the third descent point. With the structural approach proposed here, one can further characterize other third and fourth descent points of the k-error linear complexity for 2n- periodic binary sequences.