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On the k-Error Linear Complexity of Binary Sequences Derived from the Discrete Logarithm in Finite Fields
Joint Authors
Source
Issue
Vol. 2019, Issue 2019 (31 Dec. 2019), pp.1-7, 7 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2019-07-04
Country of Publication
Egypt
No. of Pages
7
Main Subjects
Abstract EN
Let Fq be the finite field with q=pr elements, where p is an odd prime.
For the ordered elements ξ0,ξ1,…,ξq-1∈Fq, the binary sequence σ=(σ0,σ1,…,σq-1) with period q is defined over the finite field F2={0,1} as follows: σn=0, if n=0, (1-χ(ξn))/2, if 1≤n Obviously, σ is the Legendre sequence if r=1. In this paper, our first contribution is to prove a lower bound on the linear complexity of σ for r≥2, which improves some results of Meidl and Winterhof. Our second contribution is to study the distribution of the k-error linear complexity of σ for r=2. Unfortunately, the method presented in this paper seems not suitable for the case r>2 and we leave it open.
American Psychological Association (APA)
Chen, Zhixiong& Wang, Qiuyan. 2019. On the k-Error Linear Complexity of Binary Sequences Derived from the Discrete Logarithm in Finite Fields. Complexity،Vol. 2019, no. 2019, pp.1-7.
https://search.emarefa.net/detail/BIM-1133010
Modern Language Association (MLA)
Chen, Zhixiong& Wang, Qiuyan. On the k-Error Linear Complexity of Binary Sequences Derived from the Discrete Logarithm in Finite Fields. Complexity No. 2019 (2019), pp.1-7.
https://search.emarefa.net/detail/BIM-1133010
American Medical Association (AMA)
Chen, Zhixiong& Wang, Qiuyan. On the k-Error Linear Complexity of Binary Sequences Derived from the Discrete Logarithm in Finite Fields. Complexity. 2019. Vol. 2019, no. 2019, pp.1-7.
https://search.emarefa.net/detail/BIM-1133010
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1133010