Abstract: This paper researches on orthomorphic permutation polynomials over finite fields It points out that there exist some questions about existence of orthomorphic permutation polynomials with degree 2d-1 and degree 2d over finite fields By using the congruence theory and the distributive law of degrees for multiplying polynomials, the reasons are analyzed and the questions above are solved. Results of nonexistence of orthomorphic permutation polynomials with degree 2d-1 and existence of orthomorphic permutation polynomials with degree 2d over finite field are revised.

Key words: finite field, orthomorphic permutation, polynomial

摘要： 研究有限域 上的正形置换多项式，针对有限域 上2d-1次和2d次正形置换多项式存在性的问题，利用同余类知识和有限域上乘积多项式的次数分布规律，分析其原因并给出有限域 上2d-1次正形置换多项式不存在和2d次正形置换多项式存在的判定结果。

关键词: 有限域, 正形置换, 多项式

CLC Number: 

• TN918.1