四川师范大学学报（自然科学版）2011，Vol.34Issue(3)：289-295,封2,8.DOI:10.3969/j.issn.1001-8395.2011.03.002
有限域上的k-型高斯正规基及其对偶基
The Type k-Gaussian Normal Bases over Finite Fields and Their Dual Bases
摘要
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 s 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.关键词
有限域/高斯正规基/对偶基/复杂度Key words
finite field/ Gaussian period normal basis/ dual basis/ complexity分类
数理科学引用本文复制引用
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,封2,8.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)和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 （10990011）
