| 有限域上的2-型高斯正规基及其对偶基(英文) |
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| 引用本文： | 廖群英,苏丹丹,付萍. 有限域上的2-型高斯正规基及其对偶基(英文)[J]. 四川大学学报(自然科学版), 2010, 47(6): 1221-1224. DOI: 10.3969/j.issn.0490-6756.2010.06.005 |
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| 作者姓名： | 廖群英 苏丹丹 付萍 |
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| 作者单位： | 四川师范大学数学与软件科学学院,成都,610066 |
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| 基金项目： | 国家自然科学基金科研重大项目(10990011);教育部博士点科研专项基金新教师课题基金(20095134120001);四川省教育厅自然科学科研重点项目(09ZA087) |
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| 摘 要： | 设q为素数p的幂,F_q~n为有限域F_q的n(n≥2)次扩域.熟知k-型高斯正规基当k=1时为Ⅰ型最优正规基,当q=k=2时为Ⅱ型最优正规基.本文证明了k-型高斯正规基生成元的迹函数为-1,确定了2-型高斯正规基的复杂度及其对偶基的生成元与复杂度.
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| 关 键 词： | 有限域 高斯正规基 对偶基 本原元 复杂度 |
| 收稿时间： | 2009-08-09 |
The type 2 Gaussian normal basis and its dual basis over finite fields |
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| LIAO Qun-Ying,SU Dan-Dan,FU Ping. The type 2 Gaussian normal basis and its dual basis over finite fields[J]. Journal of Sichuan University (Natural Science Edition), 2010, 47(6): 1221-1224. DOI: 10.3969/j.issn.0490-6756.2010.06.005 |
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| Authors: | LIAO Qun-Ying SU Dan-Dan FU Ping |
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| Affiliation: | College of Mathematics and Software Science, Sichuan Normal University;College of Mathematics and Software Science, Sichuan Normal University;College of Mathematics and Software Science, Sichuan Normal University |
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| Abstract: | Let q be a power of the prime p and Fnq the extension of the finite field Fq with degree n(n≥2).It's well-known that the type k Gaussian normal basis of Fnq over Fq is a type Ⅰ or type Ⅱ optimal normal basis depends on k=1 or q=k=2 correspondingly.In the present paper,the authors prove that the trace of a generator of the type k Gaussian normal basis of Fnq over Fq equals to-1.For the case k=2,they determine the dual basis B of N and the complexities for N and B. |
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| Keywords: | finite field Gaussian normal basis dual basis primitive element complexity |
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