有限域上一类非零迹不可约多项式的计数公式  

Counting formulas for a class of irreducible polynomials with non-zero traces over finite fields

作　　者：刘石荣 谢炜涛 LIU Shirong;XIE Weitao(School of Mathematics and Statistic,Minnan Normal University,Zhangzhou,Fujian 363000,China)

机构地区：[1]闽南师范大学数学与统计学院,福建漳州363000

出　　处：《闽南师范大学学报（自然科学版）》2023年第3期73-77,共5页Journal of Minnan Normal University：Natural Science

基　　金：福建省自然科学基金(2022J02046).

摘　　要：利用有限域上多项式普通分解与其相伴的线性化多项式符号分解之间的关系,研究有限域上一类非零迹不可约多项式.由此得到了其计数公式,并推导出两个已知的结论.The paper makes a study of a class of irreducible polynomials with non-zero traces over finite fields by using the relationship between the ordinary factorization of a given polynomial and the symbolic factorization of its linearized associate,and obtains the counting formulas for such polynomials,from which two well-known results can be derived.

关 键 词：有限域 不可约多项式 线性化多项式 

分 类 号：O156[理学—数学]