scholarly journals On Weil Sums, Conjectures of Helleseth, and Niho Exponents

2021 ◽  
Author(s):  
Liem Nguyen
Keyword(s):  
Niho Exponents ◽  
Weil Sums

Several classes of permutation trinomials from Niho exponents over finite fields of characteristic 3

2019 ◽  
Vol 18 (04) ◽  
pp. 1950069
Author(s):  
Qian Liu ◽  
Yujuan Sun
Keyword(s):  
Positive Integer ◽  
Finite Field ◽  
Coding Theory ◽  
Permutation Polynomials ◽  
Combinatorial Designs ◽  
Dickson Polynomial ◽  
Niho Exponents ◽  
Characteristic 3 ◽  
Permutation Trinomials ◽  
Algebraic Forms

Permutation polynomials have important applications in cryptography, coding theory, combinatorial designs, and other areas of mathematics and engineering. Finding new classes of permutation polynomials is therefore an interesting subject of study. Permutation trinomials attract people’s interest due to their simple algebraic forms and additional extraordinary properties. In this paper, based on a seventh-degree and a fifth-degree Dickson polynomial over the finite field [Formula: see text], two conjectures on permutation trinomials over [Formula: see text] presented recently by Li–Qu–Li–Fu are partially settled, where [Formula: see text] is a positive integer.

On the dual of bent functions with 2r Niho exponents

2011 ◽  
Author(s):  
Claude Carlet ◽  
Tor Helleseth ◽  
Alexander Kholosha ◽  
Sihem Mesnager
Keyword(s):  
Bent Functions ◽  
Niho Exponents

scholarly journals Proof of a conjectured three-valued family of Weil sums of binomials

2015 ◽  
Vol 169 (2) ◽  
pp. 181-199 ◽  
Author(s):  
Daniel J. Katz ◽  
Philippe Langevin
Keyword(s):  
Weil Sums

A survey on the applications of Niho exponents

2018 ◽  
Vol 11 (3) ◽  
pp. 509-548 ◽  
Author(s):  
Nian Li ◽  
Xiangyong Zeng
Keyword(s):  
Niho Exponents

scholarly journals Further evaluations of Weil sums

1998 ◽  
Vol 86 (3) ◽  
pp. 217-226 ◽  
Author(s):  
Robert Coulter
Keyword(s):  
Weil Sums

scholarly journals Explicit evaluations of some Weil sums

1998 ◽  
Vol 83 (3) ◽  
pp. 241-251 ◽  
Author(s):  
Robert Coulter
Keyword(s):  
Weil Sums
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