A new lower bound on the family complexity of Legendre sequences

Date

2020-06-01

Author

Cakiroglu, Yagmur
Yayla, Oğuz

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In this paper we study a family of Legendre sequences and its pseudo-randomness in terms of their family complexity. We present an improved lower bound on the family complexity of a family based on the Legendre symbol of polynomials over a finite field. The new bound depends on the LambertWfunction and the number of elements in a finite field belonging to its proper subfield. Moreover, we present another lower bound which is a simplified version and approximates the new bound. We show that both bounds are better than previously known ones.

Subject Keywords

Algebra and Number Theory, Applied Mathematics

URI

https://hdl.handle.net/11511/69850

Journal

APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING

DOI

https://doi.org/10.1007/s00200-020-00442-y

Collections

Graduate School of Applied Mathematics, Article

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Citation Formats

Y. Cakiroglu and O. Yayla, “A new lower bound on the family complexity of Legendre sequences,” APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, pp. 0–0, 2020, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/69850.