有限域上一类非零迹多项式的计数公式
PDF下载 (272)高 伟,黄 华,曹 炜.有限域上一类非零迹多项式的计数公式[J].宁波大学学报(理工版),2019,32(2):97-99.DOI:
GAO Wei,HUANG Hua,CAO Wei.Counting formula for a class of polynomials with nonzero traces in finite fields[J].Journal of Ningbo University(Natural Science & Engineering Edition),2019,32(2):97-99.DOI:
| Title: | Counting formula for a class of polynomials with nonzero traces in finite fields |
| 作者: | 高 伟, 黄 华, 曹 炜 |
| Author(s): | GAO Wei, HUANG Hua, CAO Wei |
| 关键词: | 有限域; 不可约多项式; 线性化多项式; 符号分解 |
| Keywords: | finite field; irreducible polynomial; linearized polynomial; symbolic factorization |
| 分类号: | O156.1 |
| 文献标识码: | A |
| 摘要: | 设 为q元有限域. 上n次多项式f(x)的迹定义为 的系数. 本文利用 中多项式的普通分解与其线性q-相伴式的符号分解之间的关系, 研究了 上非零迹多项式并得到了一类非零迹多项式的计数公式. |
| Abstract: | Let be the finite fields of q elements, and the trace of a degree n polynomial f(x) over is defined to be the coefficient of .Using the relationship between the ordinary factorization of a given poly- nomial and the symbolic factorization of its linearized q-associate, the polynomials with nonzero traces over is investigated and the counting formula is thus obtained for a class of polynomials with nonzero traces over . |
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| 备注/Memo: | 收稿日期: 2018－03－12. 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）; 宁波市自然科学基金（2017A610134）. 第一作者: 高伟（1995－）, 男, 安徽安庆人, 在读硕士研究生, 主要研究方向: 数论. E-mail: 912664929@qq.com 宁波大学学报（理工版）网址：http://journallg.nbu.edu.cn/*通信作者: 曹炜（1974－）, 男, 湖北潜江人, 博士/教授, 主要研究方向: 代数、数论. E-mail: caowei@nbu.edu.cn |
