Welcome to Journal of University of Chinese Academy of Sciences,Today is

Journal of University of Chinese Academy of Sciences ›› 2015, Vol. 32 ›› Issue (1): 9-12.DOI: 10.7523/j.issn.2095-6134.2015.01.002

Previous Articles     Next Articles

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 Online: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)

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

CLC Number: