Constructions of complete permutation polynomials

Based on the Feistel and MISTY structures, this paper presents several new constructions of complete permutation polynomials (CPPs) of the finite field \({\mathbb {F}}_{2^{n}}^2\) for a positive integer n and three constructions of CPPs over \({\mathbb {F}}_{p^{n}}^m\) for any prime p and positive integer \(m\ge 2\). In addition, we investigate the upper bound on the algebraic degree of these CPPs and show that some of them can have nearly optimal algebraic degree.