Fibonacci多项式的置换性质

Permutation properties of the Fibonacci polynomials

置换多项式在代数学、组合学、数论、编码理论、密码学等领域中均有广泛而又重要的应用.本文主要研究Fibonacci多项式.通过计算其函数值的等幂和,本文得到了判定这些定义在有限域上的Fibonacci多项式为置换多项式的必要条件,解决了Fernando和Rashid提出的一个公开问题,从而推广了有关Fibonacci多项式置换性的已有结论.

Permutation polynomial has wide and important applications in algebra,combinatorics,number theory,coding theory,cryptography,etc.In this paper,by calculating the sum of the Fibonacci polynomial,we obtain some necessary conditions that a Fibonacci polynomial,defined on a finite field,is a permutation polynomial,solve the open problem introduced by Fernando and Rashid and generalize the existing results.