A divided-difference characterization of polynomials over finite fields of characteristic two

2022 ◽  
Author(s):  
Veasna Kim ◽  
Vichian Laohakosol ◽  
Sukrawan Mavecha
Keyword(s):  
Finite Fields ◽  
Divided Difference ◽  
Polynomials Over Finite Fields ◽  
Characteristic Two

scholarly journals Some notes on the k-normal elements and k-normal polynomials over finite fields

2017 ◽  
Vol 16 (01) ◽  
pp. 1750006 ◽  
Author(s):  
Mahmood Alizadeh
Keyword(s):  
Finite Fields ◽  
Infinite Sequence ◽  
Infinite Family ◽  
Recursive Method ◽  
Polynomials Over Finite Fields ◽  
Normal Element

Recently, the [Formula: see text]-normal elements over finite fields are defined and characterized by Huczynska et al. In this paper, we give a new characterization of [Formula: see text]-normal elements and define [Formula: see text]-normal polynomials over finite fields. In what follows, we show that the problem of existence of a primitive 1-normal element in [Formula: see text] over [Formula: see text], for all [Formula: see text] and [Formula: see text], which has been stated by Huczynska et al., is not satisfied. Furthermore, we extend a recursive method given by Kyuregyan for constructing an infinite family of [Formula: see text]-polynomials, to constructing an infinite sequence of [Formula: see text]-normal polynomials over [Formula: see text].

scholarly journals Representations of polynomials over finite fields of characteristic two as A2+A+BC+D3

2007 ◽  
Vol 13 (3) ◽  
pp. 648-658 ◽  
Author(s):  
Luis Gallardo ◽  
Olivier Rahavandrainy ◽  
Leonid Vaserstein
Keyword(s):  
Finite Fields ◽  
Polynomials Over Finite Fields ◽  
Characteristic Two

Some primitive polynomials over finite fields

2001 ◽  
Vol 21 (3) ◽  
pp. 412-416 ◽  
Author(s):  
Seunghwan Chang ◽  
June Bok Lee
Keyword(s):  
Finite Fields ◽  
Primitive Polynomials ◽  
Polynomials Over Finite Fields

scholarly journals Factorization of a class of polynomials over finite fields

2012 ◽  
Vol 18 (1) ◽  
pp. 108-122 ◽  
Author(s):  
Henning Stichtenoth ◽  
Alev Topuzoğlu
Keyword(s):  
Finite Fields ◽  
Polynomials Over Finite Fields

scholarly journals Value sets of polynomials over finite fields

1993 ◽  
Vol 119 (3) ◽  
pp. 711-711 ◽  
Author(s):  
Da Qing Wan ◽  
Peter Jau-Shyong Shiue ◽  
Ching Shyang Chen
Keyword(s):  
Finite Fields ◽  
Polynomials Over Finite Fields ◽  
Value Sets
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