|
|||||
|
|
| Normal Bases and Their Dual-Bases over Finite Fields | |
| 引用本文： | Qun Ying LIAO Qi SUN. Normal Bases and Their Dual-Bases over Finite Fields[J]. 数学学报(英文版), 2006, 22(3): 845-848. DOI: 10.1007/s10114-005-0613-6 |
| 作者姓名： | Qun Ying LIAO Qi SUN |
| 作者单位： | [1]The Mathematical College of Sichuan University, Chengdu 610064, P. R. China [2]The Mathematical and Soft-Ware Scientific College of Sichuan Normal University, Chengdu 610066, P. R. China |
| 基金项目： | This work is supported by NSFC, Grant No. 10128103 |
| 摘 要： | In this paper, we prove the following results： 1） A normal basis N over a finite field is equivalent to its dual basis if and only if the multiplication table of N is symmetric; 2） The normal basis N is self-dual if and only if its multiplication table is symmetric and Tr（α^2） = 1, where α generates N; 3） An optimal normal basis N is self-dual if and only if N is a type-Ⅰ optimal normal basis with q = n = 2 or N is a type-Ⅱ optimal normal basis. |
| 关 键 词： | 最优正规基 有限场 均衡性 代数学 |
| 收稿时间： | 2004-02-25 |
| 修稿时间： | 2004-02-252004-09-27 |
Normal Bases and Their Dual–Bases over Finite Fields |
|
| Qun Ying Liao,Qi Sun. Normal Bases and Their Dual–Bases over Finite Fields[J]. Acta Mathematica Sinica(English Series), 2006, 22(3): 845-848. DOI: 10.1007/s10114-005-0613-6 | |
| Authors: | Qun Ying Liao Qi Sun |
| Affiliation: | (1) The Mathematical College of Sichuan University, Chengdu 610064, P. R. China;(2) The Mathematical and Soft-Ware Scientific College of Sichuan Normal University, Chengdu 610066, P. R. China;(3) The Mathematical College of Sichuan University, Chengdu 610064, P. R. China |
| Abstract: | In this paper, we prove the following results: 1) A normal basis N over a finite field is equivalent to its dual basis if and only if the multiplication table of N is symmetric; 2) The normal basis N is self–dual if and only if its multiplication table is symmetric and Tr(α2) = 1, where α generates N; 3) An optimal normal basis N is self–dual if and only if N is a type–I optimal normal basis with q = n = 2 or N is a type–II optimal normal basis. This work is supported by NSFC, Grant No. 10128103 |
| Keywords: | Normal bases over finite fields Optimal normal bases Multiplication tables of normal bases |
| 本文献已被 维普 SpringerLink 等数据库收录！ | |