有限域上几类多项式与迹函数复合的零点问题(英文)  

Zeros of compositions of the trace function and some special classes of polynomials over a finite field

作　　者：郑嘉[1] 吴保峰[2] 

机构地区：[1]中国科学院大学数学科学学院,北京101408 [2]中国科学院信息工程研究所信息安全国家重点实验室,北京100093

出　　处：《中国科学院大学学报（中英文）》2015年第1期9-12,30,共5页Journal of University of Chinese Academy of Sciences

基　　金：Supported by the National Natural Science Foundation of China(11271363,60970152);National 973 Program of China(2011CB302400);Strategic Priority Research Program of the Chinese Academy of Sciences(XDA06010701)

摘　　要：像集在反映有限域上多项式性质方面具有重要作用.本文刻画了有限域上像集包含于迹函数的核空间内的多项式,即复合到迹函数后以整个有限域为零点集的多项式.特别地,针对单项式、线性化多项式、DO型多项式,利用多项式自身的特点给出更加简洁的等价条件.Value sets are of importance in implying properties of polynomials over a finite field. In this paper, we characterize polynomials over a finite field with value sets contained in the kernel of the trace functions, i. e. , polynomials which have the whole finite field as zeros after incorporated in the trace function. In particular, simpler equivalent conditions about monomials, linearized polynomials, and DO polynomials are given based on their own properties.

关 键 词：多项式 像集 迹函数 零点 

分 类 号：O29[理学—应用数学]