Structure analysis on the k-error linear complexity for 2n-periodic binary sequences
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 c...
| Main Authors: | , , |
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| Format: | Journal Article |
| Published: |
American Institute of Mathematical Sciences
2017
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| Online Access: | http://hdl.handle.net/20.500.11937/57927 |
| Summary: | 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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