On the Existence for Some Special Primitive Elements in Finite Fields

被引：7

作者：

Liao, Qunying ^{[1
]}

Li, Jiyou ^{[2
]}

Pu, Keli ^{[3
]}

机构：

[1] Sichuan Normal Univ, Coll Math & Software Sci, Chengdu 610066, Peoples R China

[2] Shanghai Jiao Tong Univ, Dept Math, Shanghai 200240, Peoples R China

[3] Aba Teachers Coll, Dept Math & Finance Econ, Aba 623000, Sichuan, Peoples R China

来源：

CHINESE ANNALS OF MATHEMATICS SERIES B | 2016年 / 37卷 / 02期

基金：

中国国家自然科学基金; 上海市自然科学基金;

关键词：

Finite field; Primitive element; Normal basis; NORMAL POLYNOMIALS; BASES;

D O I：

10.1007/s11401-016-0949-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let F-q be a finite field of characteristic p. In this paper, by using the index sum method the authors obtain a sufficient condition for the existence of a primitive element alpha is an element of F-qn such that alpha + alpha(-1) is also primitive or alpha + alpha(-1) is primitive and alpha is a normal element of F-qn over F-q.

引用

页码：259 / 266

页数：8

共 50 条

[31] PRIMITIVE ELEMENTS OF GALOIS EXTENSIONS OF FINITE-FIELDS
KIKUMASA, I
NAGAHARA, T
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1992, 115 (03) : 593 - 600
[32] On the existence of some special primitive roots mod p
Han, Di
Zhang, Wenpeng
BULLETIN MATHEMATIQUE DE LA SOCIETE DES SCIENCES MATHEMATIQUES DE ROUMANIE, 2015, 58 (01): : 59 - 66
[33] On special pairs of primitive elements over a finite field
Carvalho, Cicero
Guardieiro, Joao Paulo
Neumann, Victor G. L.
Tizziotti, Guilherme
FINITE FIELDS AND THEIR APPLICATIONS, 2021, 73
[34] On the existence of r-primitive pairs (α, f (α)) in finite fields
Zhang, Hanglong
Cao, Xiwang
APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, 2024, 35 (06) : 725 - 738
[35] EXISTENCE OF RATIONAL PRIMITIVE NORMAL PAIRS OVER FINITE FIELDS
Sharma, Rajendra Kumar
Takshak, Soniya
Awasthi, Ambrish
Sharma, Hariom
INTERNATIONAL JOURNAL OF GROUP THEORY, 2024, 13 (01)
[36] Existence of primitive pairs with prescribed traces over finite fields
Sharma, Hariom
Sharma, R. K.
COMMUNICATIONS IN ALGEBRA, 2021, 49 (04) : 1773 - 1780
[37] ON PRIMITIVE ELEMENTS IN FINITE-FIELDS AND ON ELLIPTIC-CURVES
SHPARLINSKII, IE
MATHEMATICS OF THE USSR-SBORNIK, 1992, 71 (01): : 41 - 50
[38] Pair of primitive elements with prescribed traces over finite fields
Sharma, R. K.
Gupta, Anju
COMMUNICATIONS IN ALGEBRA, 2019, 47 (03) : 1278 - 1286
[39] EXISTENCE RESULTS FOR PRIMITIVE ELEMENTS IN CUBIC AND QUARTIC EXTENSIONS OF A FINITE FIELD
Bailey, Geoff
Cohen, Stephen D.
Sutherland, Nicole
Trudgian, Tim
MATHEMATICS OF COMPUTATION, 2019, 88 (316) : 931 - 947
[40] Existence of primitive pairs with two prescribed traces over finite fields
Choudhary, Aakash
Sharma, R. K.
JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2024, 23 (14)

← 1 2 3 4 5 →