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.
作者
高伟
黄华
曹炜
GAO Wei;HUANG Hua;CAO Wei(Faculty of Science,Ningbo University,Ningbo 315211,China)
出处
《宁波大学学报（理工版）》
CAS
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)
关键词
有限域
不可约多项式
线性化多项式
符号分解
finite field
irreducible polynomial
linearized polynomial
symbolic factorization
