Cube theory and k-error linear complexity profile
© 2016 SERSC. The linear complexity and k-error linear complexity of a sequence have been used as important measures for keystream strength. In order to study k-error linear complexity of binary sequences with period 2n, a new tool called cube theory is developed. In this paper, we first give a gene...
| Main Authors: | , , |
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| Format: | Journal Article |
| Published: |
2016
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| Online Access: | http://hdl.handle.net/20.500.11937/46243 |
| _version_ | 1848757505061027840 |
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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 | © 2016 SERSC. The linear complexity and k-error linear complexity of a sequence have been used as important measures for keystream strength. In order to study k-error linear complexity of binary sequences with period 2n, a new tool called cube theory is developed. In this paper, we first give a general decomposition approach to decompose a binary sequence with period 2n into some disjoint cubes. Second, a counting formula for m-cubes with the same linear complexity is derived, which is equivalent to the counting formula for k-error vectors. The counting formula of 2n-periodic binary sequences which can be decomposed into more than one cube is also investigated, which extends an important result by Etzion et al.. Finally, we study 2n-periodic binary sequences with the given k-error linear complexity profile. Consequently, the complete counting formula of 2n-periodic binary sequences with given k-error linear complexity profile of descent points 2, 4 and 6 is derived. The periodic sequences having the prescribed k-error linear complexity profile with descent points 1, 3, 5 and 7 are also briefly discussed. |
| first_indexed | 2025-11-14T09:29:09Z |
| format | Journal Article |
| id | curtin-20.500.11937-46243 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:29:09Z |
| publishDate | 2016 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-462432017-09-13T15:06:00Z Cube theory and k-error linear complexity profile Zhou, J. Liu, Wan-Quan Wang, X. © 2016 SERSC. The linear complexity and k-error linear complexity of a sequence have been used as important measures for keystream strength. In order to study k-error linear complexity of binary sequences with period 2n, a new tool called cube theory is developed. In this paper, we first give a general decomposition approach to decompose a binary sequence with period 2n into some disjoint cubes. Second, a counting formula for m-cubes with the same linear complexity is derived, which is equivalent to the counting formula for k-error vectors. The counting formula of 2n-periodic binary sequences which can be decomposed into more than one cube is also investigated, which extends an important result by Etzion et al.. Finally, we study 2n-periodic binary sequences with the given k-error linear complexity profile. Consequently, the complete counting formula of 2n-periodic binary sequences with given k-error linear complexity profile of descent points 2, 4 and 6 is derived. The periodic sequences having the prescribed k-error linear complexity profile with descent points 1, 3, 5 and 7 are also briefly discussed. 2016 Journal Article http://hdl.handle.net/20.500.11937/46243 10.14257/ijsia.2016.10.7.15 unknown |
| spellingShingle | Zhou, J. Liu, Wan-Quan Wang, X. Cube theory and k-error linear complexity profile |
| title | Cube theory and k-error linear complexity profile |
| title_full | Cube theory and k-error linear complexity profile |
| title_fullStr | Cube theory and k-error linear complexity profile |
| title_full_unstemmed | Cube theory and k-error linear complexity profile |
| title_short | Cube theory and k-error linear complexity profile |
| title_sort | cube theory and k-error linear complexity profile |
| url | http://hdl.handle.net/20.500.11937/46243 |