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

Zhixiong Chen and Qiuyan Wang

Complexity, 2019, vol. 2019, 1-7

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.

Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:hin:complx:8635209

DOI: 10.1155/2019/8635209

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