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 |
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American Institute of Mathematical Sciences
2017
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| Online Access: | http://hdl.handle.net/20.500.11937/57927 |
| _version_ | 1848760134146195456 |
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| author | Zhou, J. Liu, Wan-Quan Wang, X. |
| author_facet | Zhou, J. Liu, Wan-Quan Wang, X. |
| author_sort | Zhou, J. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T10:10:57Z |
| format | Journal Article |
| id | curtin-20.500.11937-57927 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T10:10:57Z |
| publishDate | 2017 |
| publisher | American Institute of Mathematical Sciences |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-579272023-08-02T06:39:10Z Structure analysis on the k-error linear complexity for 2n-periodic binary sequences Zhou, J. Liu, Wan-Quan Wang, X. 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. 2017 Journal Article http://hdl.handle.net/20.500.11937/57927 10.3934/jimo.2017016 American Institute of Mathematical Sciences restricted |
| spellingShingle | Zhou, J. Liu, Wan-Quan Wang, X. Structure analysis on the k-error linear complexity for 2n-periodic binary sequences |
| title | Structure analysis on the k-error linear complexity for 2n-periodic binary sequences |
| title_full | Structure analysis on the k-error linear complexity for 2n-periodic binary sequences |
| title_fullStr | Structure analysis on the k-error linear complexity for 2n-periodic binary sequences |
| title_full_unstemmed | Structure analysis on the k-error linear complexity for 2n-periodic binary sequences |
| title_short | Structure analysis on the k-error linear complexity for 2n-periodic binary sequences |
| title_sort | structure analysis on the k-error linear complexity for 2n-periodic binary sequences |
| url | http://hdl.handle.net/20.500.11937/57927 |