Abstract: Dickson polynomials are of special source of permutation polynomials over finite fields. It was found that Dickson polynomials have important applications in both pure and applied mathematics such as pseudoprimality testing and cryptology. Some new properties about Dickson polynomials are given in this note. It was shown that many properties of Dickson polynomials can be derived from our equations easily.

Key words: finite fields, Dickson polynomials, permutation polynomials

摘要： Dickson多项式是有限域上的一类重要的置换多项式，它在编码及通信领域有重要的应用，本文给出了Dickson多项式的一些新的性质，推广了一些已有的结果。

关键词: 有限域, Dickson多项式, 置换多项式