On the $ k $-error linear complexity of binary sequences of periods $ p^n $ from new cyclotomy
In this paper, we study the $ k $-error linear complexity of binary sequences with periods $ p^n $, which are derived from new generalized cyclotomic classes modulo a power of an odd prime $ p $. We establish a recursive relation and then estimate the $ k $-error linear complexity of the binary sequ...
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| Format: | Article |
| Language: | English |
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AIMS Press
2022-02-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2022446?viewType=HTML |
| _version_ | 1818488913670438912 |
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| author | Vladimir Edemskiy Chenhuang Wu |
| author_facet | Vladimir Edemskiy Chenhuang Wu |
| author_sort | Vladimir Edemskiy |
| collection | DOAJ |
| description | In this paper, we study the $ k $-error linear complexity of binary sequences with periods $ p^n $, which are derived from new generalized cyclotomic classes modulo a power of an odd prime $ p $. We establish a recursive relation and then estimate the $ k $-error linear complexity of the binary sequences with periods $ p^n $, the results extend the case $ p^2 $ that has been studied in an earlier work of Wu et al. at 2019. Our results show that the $ k $-error linear complexity of these sequences does not decrease dramatically for $ k < (p^{n}-p^{n-1})/2 $. |
| first_indexed | 2024-12-10T16:57:13Z |
| format | Article |
| id | doaj.art-90d982abd3b349b5909862f799da3dd2 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-10T16:57:13Z |
| publishDate | 2022-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-90d982abd3b349b5909862f799da3dd22022-12-22T01:40:41ZengAIMS PressAIMS Mathematics2473-69882022-02-01757997801110.3934/math.2022446On the $ k $-error linear complexity of binary sequences of periods $ p^n $ from new cyclotomyVladimir Edemskiy0Chenhuang Wu11. Department of Applied Mathematics and Information Science, Yaroslav-the-Wise Novgorod State University, Veliky Novgorod, 173003, Russia2. Provincial Key Laboratory of Applied Mathematics, Putian University, Putian, Fujian 351100, China 3. School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, ChinaIn this paper, we study the $ k $-error linear complexity of binary sequences with periods $ p^n $, which are derived from new generalized cyclotomic classes modulo a power of an odd prime $ p $. We establish a recursive relation and then estimate the $ k $-error linear complexity of the binary sequences with periods $ p^n $, the results extend the case $ p^2 $ that has been studied in an earlier work of Wu et al. at 2019. Our results show that the $ k $-error linear complexity of these sequences does not decrease dramatically for $ k < (p^{n}-p^{n-1})/2 $.https://www.aimspress.com/article/doi/10.3934/math.2022446?viewType=HTMLk-error linear complexitybinary sequencescyclotomystream ciphercryptography |
| spellingShingle | Vladimir Edemskiy Chenhuang Wu On the $ k $-error linear complexity of binary sequences of periods $ p^n $ from new cyclotomy AIMS Mathematics k-error linear complexity binary sequences cyclotomy stream cipher cryptography |
| title | On the $ k $-error linear complexity of binary sequences of periods $ p^n $ from new cyclotomy |
| title_full | On the $ k $-error linear complexity of binary sequences of periods $ p^n $ from new cyclotomy |
| title_fullStr | On the $ k $-error linear complexity of binary sequences of periods $ p^n $ from new cyclotomy |
| title_full_unstemmed | On the $ k $-error linear complexity of binary sequences of periods $ p^n $ from new cyclotomy |
| title_short | On the $ k $-error linear complexity of binary sequences of periods $ p^n $ from new cyclotomy |
| title_sort | on the k error linear complexity of binary sequences of periods p n from new cyclotomy |
| topic | k-error linear complexity binary sequences cyclotomy stream cipher cryptography |
| url | https://www.aimspress.com/article/doi/10.3934/math.2022446?viewType=HTML |
| work_keys_str_mv | AT vladimiredemskiy onthekerrorlinearcomplexityofbinarysequencesofperiodspnfromnewcyclotomy AT chenhuangwu onthekerrorlinearcomplexityofbinarysequencesofperiodspnfromnewcyclotomy |