YE Zhifan, KE Pinhui, CHEN Zhixiong. Linear Complexity of d-Ary Sequence Derived from Euler Quotients over GF(q)[J]. Chinese Journal of Electronics, 2019, 28(3): 529-534. doi: 10.1049/cje.2019.02.004
Citation: YE Zhifan, KE Pinhui, CHEN Zhixiong. Linear Complexity of d-Ary Sequence Derived from Euler Quotients over GF(q)[J]. Chinese Journal of Electronics, 2019, 28(3): 529-534. doi: 10.1049/cje.2019.02.004

Linear Complexity of d-Ary Sequence Derived from Euler Quotients over GF(q)

doi: 10.1049/cje.2019.02.004
Funds:  This work is supported by the National Natural Science Foundation of China (No.61772292, No.61772476), the Provincial Natural Science Foundation of Fujian (No.2019J01273) and the Foundation of Fujian Educational Committee (No.JAT170627).
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  • Corresponding author: KE Pinhui (corresponding author) received the Ph.D. degree in Cryptography from Beijing University of Posts and Telecommunications in 2006. He is now a professor of Fujian Normal University. His research interests include sequence design and algebraic coding. (Email:keph@fjnu.edu.cn)
  • Received Date: 2017-04-18
  • Publish Date: 2019-05-10
  • For an odd prime p and positive integers r, d such that 0 < dpr, a generic construction of dary sequence based on Euler quotients is presented in this paper. Compared with the known construction, in which the support set of the sequence is fixed and d is usually required to be a prime, the support set of the proposed sequence is flexible and d could be any positive integer less then pr in our construction. Furthermore, the linear complexity of the proposed sequence over prime field GF(q) with the assumption of qp-1 ≢ 1 mod p2 is determined. An algorithm of computing the linear complexity of the sequence is also given. Our results indicate that, with some constrains on the support set, the new sequences possess large linear complexities.
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