| 有限域上的k-型高斯正规基及其对偶基 |
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| 引用本文： | 李俊,黄琴,李波,廖群英. 有限域上的k-型高斯正规基及其对偶基[J]. 四川师范大学学报(自然科学版), 2011, 34(3): 289-295. DOI: 10.3969/j.issn.1001-8395.2011.03.002 |
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| 作者姓名： | 李俊 黄琴 李波 廖群英 |
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| 作者单位： | 四川师范大学数学与软件科学学院,四川成都,610066 |
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| 基金项目： | 国家自然科学基金重大项目(10990011); 教育部博士点专项基金(2009513420001); 四川省教育厅自然科学重点基金(09ZA087); 四川省杰出青年学术技术带头人培育计划基金(2011JQ0037)资助项目 |
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| 摘 要： | 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(Finite Fields and their Applications,2007,13(4):417-417.)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...
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| 关 键 词： | 有限域 高斯正规基 对偶基 复杂度 |
The Type k-Gaussian Normal Bases over Finite Fields and Their Dual Bases |
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| LI Jun,HUANG Qin,LI Bo,LIAO Qun-ying. The Type k-Gaussian Normal Bases over Finite Fields and Their Dual Bases[J]. Journal of Sichuan Normal University(Natural Science), 2011, 34(3): 289-295. DOI: 10.3969/j.issn.1001-8395.2011.03.002 |
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| Authors: | LI Jun HUANG Qin LI Bo LIAO Qun-ying |
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| Affiliation: | LI Jun,HUANG Qin,LI Bo,LIAO Qun-ying(College of Mathematics and Software Science,Sichuan Normal University,Chengdu 610066,Sichuan) |
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| Abstract: | It is well-known that normal bases are widely used in applications of finite fields in areas such as coding theory,cryptography,signal processing,and so on.Z.X.Wan et al(Finite Fields and Their Applications,2007,13(4):411-417.) computed the complexity of the dual basis of a type Ⅰ optimal normal basis of Fqn over Fq which is equal to 3n-2 or 3n-3 according to q is odd or even,respectively.This is a special class of type k-Gaussian normal bases.Recently,Q.Y.Liao et al(J.Sichuan University:Science Nautural,2010,47(6):1221-1224.) gave the dual basis and the complexity of a type 2-Gaussian normal basis.In this paper,for a general type k-Gaussian normal basis N,we obtain the dual basis and a upper bound for the complexity of N when n≥ k≥ 1.Furthermore,we prove that the upper bound can be achieved for k=3,and then determine all(weakly) self-dual type k-Gaussian normal bases. |
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| Keywords: | finite field Gaussian period normal basis dual basis complexity |
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