A new lower bound on the family complexity of Legendre sequences

Date

2020-06-01

Author

Cakiroglu, Yagmur
Yayla, Oğuz

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

233
views

0
downloads

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

Suggestions

OpenMETU
Core

A specific type of permutation and complete permutation polynomials over finite fields Ongan, Pinar; GÜLMEZ TEMÜR, BURCU (World Scientific Pub Co Pte Lt, 2020-04-01) In this paper, we study polynomials of the form f(x) = x (qn-1/q-1+1) + bx is an element of F-qn[x], where n = 5 and list all permutation polynomials (PPs) and complete permutation polynomials (CPPs) of this form. This type of polynomials were studied by Bassalygo and Zinoviev for the cases n = 2 and n = 3, Wu, Li, Helleseth and Zhang for the case n = 4, p not equal 2, Bassalygo and Zinoviev answered the question for the case n = 4, p= 2 and finally by Bartoli et al. for the case n = 6. Here, we determine a...
A generic identification theorem for L*-groups of finite Morley rank Berkman, Ayse; Borovik, Alexandre V.; Burdges, Jeffrey; Cherfin, Gregory (Elsevier BV, 2008-01-01) This paper provides a method for identifying "sufficiently rich" simple groups of finite Morley rank with simple algebraic groups over algebraically closed fields. Special attention is given to the even type case, and the paper contains a number of structural results about simple groups of finite Morley rank and even type.
An identification theorem for groups of finite Morley rank and even type Berkman, A; Borovik, AV (Elsevier BV, 2003-08-15) The paper contains a construction of a definable BN-pair in a simple group of finite Morley rank and even type with a sufficiently good system of 2-local parabolic subgroups. This provides 'the final identification theorem' for simple groups of finite Morley rank and even type.
On the deformation chirality of real cubic fourfolds Finashin, Sergey (Wiley, 2009-09-01) According to our previous results, the conjugacy class of the involution induced by the complex conjugation in the homology of a real non-singular cubic fourfold determines the fourfold tip to projective equivalence and deformation. Here, we show how to eliminate the projective equivalence and obtain a pure deformation classification, that is, how to respond to the chirality problem: which cubics are not deformation equivalent to their image under a mirror reflection. We provide an arithmetical criterion of...
A technical note on weak shift equivalence Tezer, Cem (Elsevier BV, 1999-06-01) Weak shift equivalence which arises in the dynamical study of certain attractors is shown to be an equivalence relation among group endomorphisms. (C) 1999 Academic Press.

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.