线性化多项式核的刻画  

Characterizations of Kernel of Linearized Polynomials

作　　者：郭嘉鑫 金永 

机构地区：[1]中国民航大学理学院,天津

出　　处：《理论数学》2024年第8期153-161,共9页Pure Mathematics

摘　　要：本文在总结相关文献的基础上,整理了Fqn上的线性化多项式核的多种刻画方式。首先,总结了Fq上线性化多项式代数L(Fq)的循环矩阵刻画。接着在回顾了线性化多项式的“迹表示”后,通过“迹表示”及初等方法证明了Dickson关于线性化置换多项式的知名判定法则,并再次得到了Fqn上的线性化多项式代数与Dickson矩阵代数间的同构关系。In this paper, we summarize some characterizations of the kernel of linearized polynomials over Fqnafter reviewing related articles. Firstly, circulant matrices characterization of algebra L(Fq)over Fqare summed up. Then, after reviewing the “trace representations” of linearized polynomials, we prove Dickson’s well-known decision rule for permutation linearized polynomials by elementary methods and “trace representations”, then obtain the isomorphism between linearized polynomials algebra and Dickson matrices algebra over Fqnagain.

关 键 词：线性化多项式 Dickson矩阵 迹表示 循环矩阵 

分 类 号：O15[理学—数学]