Normal high order elements in finite field extensions based on the cyclotomic polynomials

被引：2

作者：

Popovych, R. ^{[1
]}

Skuratovskii, R. ^{[2
]}

机构：

[1] Lviv Polytech Natl Univ, Inst Comp Technol, Bandery Str 12, UA-79013 Lvov, Ukraine

[2] Igor Sikorsky Kiev Polytech Inst, Ave Pobedy, UA-03056 Kiev, Ukraine

来源：

ALGEBRA AND DISCRETE MATHEMATICS | 2020年 / 29卷 / 02期

关键词：

finite field; cyclotomic polynomial; normal basis; high multiplicative order element;

D O I：

10.12958/adm1117

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider elements which are both of high multiplicative order and normal in extensions F-qm of the field F-q. If the extension is defined by a cyclotomic polynomial, we construct such elements explicitly and give explicit lower bounds on their orders.

引用

页码：241 / 248

页数：8

共 9 条

[1] MULTIPLICATIVE ORDER OF GAUSS PERIODS [J].

Ahmadi, Omran ;

Shparlinski, Igor E. ;

Voloch, Jose Felipe .

INTERNATIONAL JOURNAL OF NUMBER THEORY, 2010, 6 (04) :877-882

[2] Existence and properties of k-normal elements over finite fields [J].

Huczynska, Sophie ;

Mullen, Gary L. ;

Panario, Daniel ;

Thomson, David .

FINITE FIELDS AND THEIR APPLICATIONS, 2013, 24 :170-183

[3]

Jungnickel D., 1996, Math. Mag, V69, P53

[4]

Lidl R., 1997, Finite Fields

[5]

Mullen Gary L., 2013, Handbook of Finite Fields, Discrete Mathematics and its Applications, V1st

[6] Sharpening of the Explicit Lower Bounds for the Order of Elements in Finite Field Extensions Based on Cyclotomic Polynomials [J].

Popovych, R. .

UKRAINIAN MATHEMATICAL JOURNAL, 2014, 66 (06) :916-927

[7] Elements of high order in finite fields of the form Fq[x]/Φr(x) [J].

Popovych, Roman .

FINITE FIELDS AND THEIR APPLICATIONS, 2012, 18 (04) :700-710

[8]

Skuratovskii R. V., 2011, B T SHEVCHENKO NA PM, P49

[9] Orders of Gauss periods in finite fields [J].

von zur Gathen, J ;

Shparlinski, I .

APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, 1998, 9 (01) :15-24

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