有限域上线性化多项式与正规基
PDF下载 (270)徐碧云,肖义丽,曹 炜.有限域上线性化多项式与正规基[J].宁波大学学报(理工版),2022,35(2):22-26.DOI:
XU Biyun,XIAO Yili,CAO Wei.Linearized polynomials and normal bases in finite fields[J].Journal of Ningbo University(Natural Science & Engineering Edition),2022,35(2):22-26.DOI:
| Title: | Linearized polynomials and normal bases in finite fields |
| 作者: | 徐碧云, 肖义丽, 曹 炜 |
| Author(s): | XU Biyun, XIAO Yili, CAO Wei |
| 关键词: | 有限域; 正规基; 线性化多项式 |
| Keywords: | finite field; normal basis; linearized polynomial |
| 分类号: | O156 |
| 文献标识码: | A |
| 摘要: | 设 为q阶有限域, 为 的 次扩域. 上形如 的一组基称为 的正规基, 此时 称为 上的正规元. 设 为 的一个正因子, 用 表示 的正规元集合, 用 表示 中满足 且 的元素 的集合. 本文利用有限域上线性化多项式的性质, 给出了 与 的计数公式. |
| Abstract: | Let be the finite field of elements, and be its extension of degree . A normal basis of over is a basis of the form and is called a normal element of . For a positive divisor of , let denote the set of all the normal elements of , denote the set of satisfying and . In this paper, we provide the counting formulae for and using properties of linearized polynomials in finite fields. |
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| 备注/Memo: | 收稿日期: 2021－04－24. 宁波大学学报（理工版）网址: http://journallg.nbu.edu.cn/ 基金项目: 国家自然科学基金（11871291）. 第一作者: 徐碧云（1996－）, 女, 广东揭阳人, 在读硕士研究生, 主要研究方向: 数论. E-mail: 675070711@qq.com *通信作者: 曹炜（1974－）, 男, 湖北潜江人, 博士/教授, 主要研究方向: 数论与密码学. E-mail: caowei@nbu.edu.cn 宁波大学学报（理工版）网址：http://journallg.nbu.edu.cn/ |
