Autocorrelation and Linear Complexity of Binary Generalized Cyclotomic Sequences with Period pq
Ding constructed a new cyclotomic class V0 ,V1. Based on it, a construction of generalized cyclotomic binary sequences with period pq is described, and their autocorrelation value, linear complexity, and minimal polynomial are confirmed. The autocorrelation function CSw is 3-level if p≡3mod4, and CS...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/5535887 |
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| _version_ | 1832546848761446400 |
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| author | Yan Wang Liantao Yan Qing Tian Liping Ding |
| author_facet | Yan Wang Liantao Yan Qing Tian Liping Ding |
| author_sort | Yan Wang |
| collection | DOAJ |
| description | Ding constructed a new cyclotomic class V0 ,V1. Based on it, a construction of generalized cyclotomic binary sequences with period pq is described, and their autocorrelation value, linear complexity, and minimal polynomial are confirmed. The autocorrelation function CSw is 3-level if p≡3mod4, and CSw is 5-level if p≡1mod4. The linear complexity LCS>pq/2 if p≡1 mod 8, p>q+1, or p≡3mod4 or p≡−3mod8. The results show that these sequences have quite good cryptographic properties in the aspect of autocorrelation and linear complexity. |
| format | Article |
| id | doaj-art-f6287e152cbb49cbb6cbcede68b68102 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-f6287e152cbb49cbb6cbcede68b681022025-02-03T06:47:04ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/55358875535887Autocorrelation and Linear Complexity of Binary Generalized Cyclotomic Sequences with Period pqYan Wang0Liantao Yan1Qing Tian2Liping Ding3School of Science, Xi’an University of Architecture and Technology, Xi’an 710055, ChinaSchool of Science, Xi’an University of Architecture and Technology, Xi’an 710055, ChinaSchool of Science, Xi’an University of Architecture and Technology, Xi’an 710055, ChinaSchool of Science, Xi’an University of Architecture and Technology, Xi’an 710055, ChinaDing constructed a new cyclotomic class V0 ,V1. Based on it, a construction of generalized cyclotomic binary sequences with period pq is described, and their autocorrelation value, linear complexity, and minimal polynomial are confirmed. The autocorrelation function CSw is 3-level if p≡3mod4, and CSw is 5-level if p≡1mod4. The linear complexity LCS>pq/2 if p≡1 mod 8, p>q+1, or p≡3mod4 or p≡−3mod8. The results show that these sequences have quite good cryptographic properties in the aspect of autocorrelation and linear complexity.http://dx.doi.org/10.1155/2021/5535887 |
| spellingShingle | Yan Wang Liantao Yan Qing Tian Liping Ding Autocorrelation and Linear Complexity of Binary Generalized Cyclotomic Sequences with Period pq Journal of Mathematics |
| title | Autocorrelation and Linear Complexity of Binary Generalized Cyclotomic Sequences with Period pq |
| title_full | Autocorrelation and Linear Complexity of Binary Generalized Cyclotomic Sequences with Period pq |
| title_fullStr | Autocorrelation and Linear Complexity of Binary Generalized Cyclotomic Sequences with Period pq |
| title_full_unstemmed | Autocorrelation and Linear Complexity of Binary Generalized Cyclotomic Sequences with Period pq |
| title_short | Autocorrelation and Linear Complexity of Binary Generalized Cyclotomic Sequences with Period pq |
| title_sort | autocorrelation and linear complexity of binary generalized cyclotomic sequences with period pq |
| url | http://dx.doi.org/10.1155/2021/5535887 |
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