EXISTENCE OF RATIONAL PRIMITIVE NORMAL PAIRS OVER FINITE FIELDS

被引：0

作者：

Sharma, Rajendra Kumar ^{[1
]}

Takshak, Soniya ^{[1
]}

Awasthi, Ambrish ^{[2
]}

Sharma, Hariom ^{[3
]}

机构：

[1] Indian Inst Technol, Dept Math, Hauz Khas, New Delhi 110016, India

[2] Def Res & Dev Org, Sci Anal Grp, Metcalfe House, Delhi 110054, India

[3] S S Govt PG Coll, Faridabad 121101, Haryana, India

来源：

INTERNATIONAL JOURNAL OF GROUP THEORY | 2024年 / 13卷 / 01期

关键词：

Finite Field; Primitive Element; Normal Element; Character; NORMAL BASES; ELEMENTS;

D O I：

10.22108/IJGT.2022.133016.1784

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

. For a finite field Fqn and a rational function f = f1 condition for the existence of a primitive normal element alpha is an element of Fqn in such a way f(alpha) is also primitive in Fqn , where f(x) is a rational function in Fqn (x) of degree sum m (degree sum of f(x) = f1 (x) f2(x) is defined to be the sum of the degrees of f1(x) and f2(x)). Additionally, for rational functions of degree sum 4, we proved that there are only 37 and 16 exceptional values of (q, n) when q = 2k and q = 3k respectively.

引用

页数：14

共 18 条

[1] Existence of some special primitive normal elements over finite fields [J].

Anju ;

Sharma, R. K. .

FINITE FIELDS AND THEIR APPLICATIONS, 2017, 46 :280-303

[2] On the Existence of Pairs of Primitive and Normal Elements Over Finite Fields [J].

Carvalho, Cicero ;

Guardieiro, Joao Paulo ;

Neumann, Victor G. L. ;

Tizziotti, Guilherme .

BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, 2022, 53 (03) :677-699

[3] Using Stepanov's method for exponential sums involving rational functions [J].

Cochrane, T ;

Pinner, C .

JOURNAL OF NUMBER THEORY, 2006, 116 (02) :270-292

[4] The primitive normal basis theorem without a computer [J].

Cohen, SD ;

Huczynska, S .

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2003, 67 :41-56

[5] Primitive element pairs with a prescribed trace in the quartic extension of a finite field [J].

Cohen, Stephen D. ;

Gupta, Anju .

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2021, 20 (09)

[6] Primitive values of rational functions at primitive elements of a finite field [J].

Cohen, Stephen D. ;

Sharma, Hariom ;

Sharma, Rajendra .

JOURNAL OF NUMBER THEORY, 2021, 219 :237-246

[7] Pairs of primitive elements in fields of even order [J].

Cohen, Stephen D. .

FINITE FIELDS AND THEIR APPLICATIONS, 2014, 28 :22-42

[8] The strong primitive normal basis theorem [J].

Cohen, Stephen D. ;

Huczynska, Sophie .

ACTA ARITHMETICA, 2010, 143 (04) :299-332

[9] A CLASS OF INCOMPLETE CHARACTER SUMS [J].

Fu, Lei ;

Wan, Daqing .

QUARTERLY JOURNAL OF MATHEMATICS, 2014, 65 (04) :1195-1211

[10] Primitive element pairs with one prescribed trace over a finite field [J].

Gupta, Anju ;

Sharma, R. K. ;

Cohen, Stephen D. .

FINITE FIELDS AND THEIR APPLICATIONS, 2018, 54 :1-14

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