全部 标题 作者
关键词 摘要

OALib Journal期刊
ISSN: 2333-9721
费用:99美元

查看量下载量

相关文章

更多...

有限域上的k-型高斯正规基及其对偶基

, PP. 289-295

Keywords: 有限域,高斯正规基,对偶基,复杂度

Full-Text   Cite this paper   Add to My Lib

Abstract:

正规基在有限域的许多应用领域中有广泛应用编码理论、密码学、信号传送等.Z.X.Wan等(FiniteFieldsandTheirApplications,2007,13(4)411-417.)给出了Fqn在Fq上的Ⅰ型最优正规基的对偶基的复杂度为3n-3(q为偶数)或3n-2(q为奇数).这是一类类似于k-型高斯正规基的低复杂度正规基.最近,廖群英等(四川大学学报自然科学版,2010,47(6)1221-1224.)给出了2-型高斯正规基的对偶基及其复杂度.在此基础上,给出了一般的k-型高斯正规基N的对偶基以及当n≥k≥1时,N的复杂度的一个上界.进而证明了当k=3时,此上界可达到,并由此给出了所有(弱)自对偶的k-型高斯正规基.

References

[1]  Mullin R, Onyszchuk I, Vanstone S, et al. Optimal normal bases in GF(pn) \[J\]. Discrete Applied Math,1988/1989,22:149-161.
[2]  Lidl R, Niederreiter H. Finite Fields and Their Applications\[M\]. Cambrige:Cambrige University Press,1994.
[3]  Nogami Y, Nasu H, Morikawa Y, et al. A method for constructing a self-dual normal basis in odd characteristic extension fields\[J\]. Finite Fields and Their Applications,2008,14(2):867-876.
[4]  Liao Q Y, Feng K Q. On the complexity of the normal bases via prime gauss period over finite fields\[J\]. J Syst Sci Complexity,2009,22(3):9-22.
[5]  Gao S H. Abelian groups,Gauss periods,and normal bases\[J\]. Finite Fields Appls, 2001,7(1):149-161.
[6]  Liao Q Y, Sun Q. Normal bases and their dual-bases over finite fields\[J\]. Acta Mathematic Sinica,2006,22(3):845-848.
[7]  廖群英,孙琦. 有限域上最优正规基的乘法表\[J\]. 数学学报,2005,48(5):947-954.
[8]  Liao Q Y. On the distribution of normal bases over finite fields\[J\]. Advances in Mathematics,2010,39(2):207-211.
[9]  Gao S H. Normal bases over finite fields\[D\]. Waterloo:Waterloo University,1993.
[10]  Wan Z X, Zhou K. On the complexity of the dual bases of a type I optimal normal bases\[J\]. Finite Fields and Their Applications,2007,13(4):411-417.
[11]  Ash D, Blake I, Vanstone S. Low complexity normal bases\[J\]. Discrete Applied Math,1999,25:191-210.
[12]  Wassermann A. Konstruktion von normalbasen\[J\]. Bayreuther Mathematische Schriften,1990,31:155-164.
[13]  Menezes AJ, Blake I F, Gao X H, et al. Applications of Finite Fields\[M\]. New York:Kluwer Academic Publishers,1993.
[14]  廖群英,孙琦. 有限域上存在弱自对偶正规基的一个充要条件\[J\]. 数学年刊,2007,A28(2):273-280.
[15]  廖群英,苏丹丹,付平. 有限域上2-型高斯正规基及其对偶基\[J\]. 四川大学学报:自然科学版,2010,47(6):1221-1224.

Full-Text

Contact Us

service@oalib.com

QQ:3279437679

WhatsApp +8615387084133