MULTIPLICATIVE ORDER OF GAUSS PERIODS

被引：22

作者：

Ahmadi, Omran ^{[1
]}

Shparlinski, Igor E. ^{[2
]}

Voloch, Jose Felipe ^{[3
]}

机构：

[1] Univ Coll Dublin, Claude Shannon Inst, Dublin 4, Ireland

[2] Macquarie Univ, Dept Comp, Sydney, NSW 2109, Australia

[3] Univ Texas Austin, Dept Math, Austin, TX 78712 USA

来源：

INTERNATIONAL JOURNAL OF NUMBER THEORY | 2010年 / 6卷 / 04期

关键词：

Finite fields; multiplicative order; Gauss period; partition; FINITE-FIELD ELEMENTS; NORMAL BASES;

D O I：

10.1142/S1793042110003290

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We obtain a lower bound on the multiplicative order of Gauss periods which generate normal bases over finite fields. This bound improves the previous bound of von zur Gathen and Shparlinski.

引用

页码：877 / 882

页数：6

共 50 条

[21] Sparse polynomials, redundant bases, Gauss periods, and efficient exponentiation of primitive elements for small characteristic finite fields
Kwon, Soonhak
Kim, Chang Hoon
Hong, Chun Pyo
DESIGNS CODES AND CRYPTOGRAPHY, 2006, 41 (03) : 299 - 306
[22] Sparse polynomials, redundant bases, gauss periods, and efficient exponentiation of primitive elements for small characteristic finite fields
Soonhak Kwon
Chang Hoon Kim
Chun Pyo Hong
Designs, Codes and Cryptography, 2006, 41 : 299 - 306
[23] LOWER BOUNDS FOR PERIODS OF DUCCI SEQUENCES
Breuer, Florian
Shparlinski, Igor E.
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2020, 102 (01) : 31 - 38
[24] Additive Patterns in Multiplicative Subgroups
Alon, Noga
Bourgain, Jean
GEOMETRIC AND FUNCTIONAL ANALYSIS, 2014, 24 (03) : 721 - 739
[25] Finding a Basis Conversion Matrix via Prime Gauss Period Normal Basis
Nogami, Yasuyuki
Namba, Ryo
Morikawa, Yoshitaka
IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES, 2009, E92A (06) : 1500 - 1507
[26] Fields with indecomposable multiplicative groups
Chebolu, Sunil K.
Lockridge, Keir
EXPOSITIONES MATHEMATICAE, 2016, 34 (02) : 237 - 242
[27] Elements of high order in finite fields of the form Fq[x]/Φr(x)
Popovych, Roman
FINITE FIELDS AND THEIR APPLICATIONS, 2012, 18 (04) : 700 - 710
[28] Bounds of Gauss sums in finite fields
Shparlinski, IE
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2004, 132 (10) : 2817 - 2824
[29] On uniformity of q-multiplicative sequences
Fan, Aihua
Konieczny, Jakub
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2019, 51 (03) : 466 - 488
[30] Elliptic periods for finite fields
Couveignes, Jean-Marc
Lercier, Reynald
FINITE FIELDS AND THEIR APPLICATIONS, 2009, 15 (01) : 1 - 22

← 1 2 3 4 5 →