| 有限域上的低复杂度正规基及其对偶基 |
| |
| 引用本文： | 苏丹丹,付萍.有限域上的低复杂度正规基及其对偶基[J].辽宁师范大学学报(自然科学版),2013(4):467-472. |
| |
| 作者姓名： | 苏丹丹 付萍 |
| |
| 作者单位： | [1]罗定职业技术学院教育系,广东罗定527200 [2]北京市昌平区回龙观中学,北京102200 |
| |
| 基金项目： | 国家自然科学基金项目（10990011） |
| |
| 摘 要： | 设q为素数的方幂，n为正整数，Fqn为有限域 Fq 的n次扩域。利用 Fq 上多项式分解和Fqn在Fq上正规基N＝｛αqi｜i＝0，1，…，n-1｝的基本性质得出一些低复杂度正规基及其对偶基 B＝｛βqi｜i＝0，1，…，n-1｝，并给出它们生成元之间的关系以及它们的乘法表T＝（ ti ，j ）和 H＝（ hi ，j ），同时得出对偶基复杂度的上界。
|
| 关 键 词： | 有限域 正规基 对偶基 乘法表 复杂度 |
Their dual bases and normal bases with low complexity over finite fields |
| |
| SU Dandan,FU Ping.Their dual bases and normal bases with low complexity over finite fields[J].Journal of Liaoning Normal University(Natural Science Edition),2013(4):467-472. |
| |
| Authors: | SU Dandan FU Ping |
| |
| Institution: | 1. Department of Education, Luoding Polytechnic, Luoding 527200, China; 2. Beijing Changping Huilongguan School, Beijing 102200,China) |
| |
| Abstract: | Let q be a power of a prime and na positive integer ,Fq the finite field with q elements ,Fqn the n-thextension of Fq .If N={αqi｜i=0 ,1 ,… ,n-1}is the dual basis of N .We obtain the dual bases for some normal bases with the complexity at most 3n-2 ,which were constructed by Blake etc .,u-sing the factorization of the polynomials cxq＋ ＋ 1 ＋ dxq -ax-b ,and also get their relationship between the generators and their multiplication tables .Furthermore ,we calculate the upper bound for the complexity of these dual bases . |
| |
| Keywords: | finite fields normal bases dual bases multiplication tables complexity |
| 本文献已被 维普 等数据库收录！ |
|
