收稿日期: 2014-01-07
修回日期: 2014-03-28
网络出版日期: 2015-01-15
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
Received date: 2014-01-07
Revised date: 2014-03-28
Online 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)
郑嘉 , 吴保峰 . 有限域上几类多项式与迹函数复合的零点问题[J]. 中国科学院大学学报, 2015 , 32(1) : 9 -12 . DOI: 10.7523/j.issn.2095-6134.2015.01.002
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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