有限域上一类非零迹多项式的计数公式  

Counting formula for a class of polynomials with nonzero traces in finite fields

作　　者：高伟 黄华 曹炜[1] GAO Wei;HUANG Hua;CAO Wei(Faculty of Science,Ningbo University,Ningbo 315211,China)

机构地区：[1]宁波大学理学院,浙江宁波315211

出　　处：《宁波大学学报（理工版）》2019年第2期97-99,共3页Journal of Ningbo University：Natural Science and Engineering Edition

基　　金：国家自然科学基金(11871291);宁波市自然科学基金(2017A610134)

摘　　要：设F_q为q元有限域.F_q上n次多项式f(x)的迹定义为x^(n-1)的系数.本文利用F_q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F_q上非零迹多项式并得到了一类非零迹多项式的计数公式.Let Fq be the finite fields of q elements, and the trace of a degree n polynomial f(x) over Fq is defined to be the coefficient of x^n-1.Using the relationship between the ordinary factorization of a given polynomial and the symbolic factorization of its linearized q-associate, the polynomials with nonzero traces overFq is investigated and the counting formula is thus obtained for a class of polynomials with nonzero traces over Fq.

关 键 词：有限域 不可约多项式 线性化多项式 符号分解 

分 类 号：O156.1[理学—数学]