Structure analysis on the k-error linear complexity for 2<sup>n</sup>-periodic binary sequences
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In this paper, in order to characterize the critical error linear complexity spectrum (CELCS) for 2 n -periodic binary sequences, we first propose a decomposition based on the cube theory. Based on the proposed k-error cube decomposition, and the famous inclusion-exclusion principle, we obtain the complete characterization of the ith descent point (critical point) of the k-error linear complexity for i = 2; 3. In fact, the proposed constructive approach has the potential to be used for constructing 2 n -periodic binary sequences with the given linear complexity and k-error linear complexity (or CELCS), which is a challenging problem to be deserved for further investigation in future.
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Complete characterization of the first descent point distribution for the k-error linear complexity of 2<sup>n</sup>-periodic binary sequencesZhou, J.; Liu, Wan-Quan; Wang, X. (2017)© 2017 AIMS. In this paper, a new constructive approach of determining the first descent point distribution for the k-error linear complexity of 2 n -periodic binary sequences is developed using the sieve method and ...
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