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On the - Error Linear Complexity of Binary Sequences Derived from the Discrete Logarithm in Finite Fields

Author

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  • Zhixiong Chen
  • Qiuyan Wang

Abstract

Let be the finite field with elements, where is an odd prime. For the ordered elements , the binary sequence with period is defined over the finite field as follows: where is the quadratic character of . Obviously, is the Legendre sequence if . In this paper, our first contribution is to prove a lower bound on the linear complexity of for , which improves some results of Meidl and Winterhof. Our second contribution is to study the distribution of the - error linear complexity of for . Unfortunately, the method presented in this paper seems not suitable for the case and we leave it open.

Suggested Citation

  • Zhixiong Chen & Qiuyan Wang, 2019. "On the - Error Linear Complexity of Binary Sequences Derived from the Discrete Logarithm in Finite Fields," Complexity, Hindawi, vol. 2019, pages 1-7, July.
    • Handle: RePEc:hin:complx:8635209
    DOI: 10.1155/2019/8635209
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