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中国科学院大学学报 ›› 2015, Vol. 32 ›› Issue (1): 9-12.DOI: 10.7523/j.issn.2095-6134.2015.01.002

• 数学与物理学 • 上一篇    下一篇

有限域上几类多项式与迹函数复合的零点问题

郑嘉1, 吴保峰2   

  1. 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
  • 收稿日期:2014-01-07 修回日期:2014-03-28 发布日期:2015-01-15
  • 通讯作者: 郑嘉
  • 基金资助:

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

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

ZHENG Jia1, WU Baofeng2   

  1. 1. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 101408, China;
    2. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100093, China
  • Received:2014-01-07 Revised:2014-03-28 Published:2015-01-15
  • Supported by:

    Supported by the National Natural Science Foundation of China (11271363, 60970152), National 973 Program of China(2011CB302400), and 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.

关键词: 多项式, 像集, 迹函数, 零点

Abstract:

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.

Key words: polynomial, value set, trace function, zero

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