关于有限域上完备映射的一个猜想的简单证明

A SIMPLE PROOF OF A CONJECTURE ABOUT COMPLETE MAPPING OVER FINITE FIELDS

Ｎｉｅｄｅｒｒｅｉｔｅｒ和Ｒｏｂｉｎｓｏｎ猜想：设Ｆｑ是一个ｑ元有限域，当ｑ＞３为偶数时，Ｆｑ上任何完备映射多项式的简化次数不超过ｑ－３．万大庆证明了这一猜想成立．运用２ａｄｉｃ数域Ｑ２，作者给出了一个简单的证明．

In 1982,Niederreiter and Robinson conjecture that if F=F q is a finite field of q elements with chF=2,q>3 ,and f(x) is a complete mapping polynomial of F, then the reduction of f(x) mod (x q-x) has degree ≤q-3 .In 1986,Wan proved this conjecture is true.In this note,by an application of 2 adic number field Q 2 ,authors give a simple proof for this conjecture.