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Constructions of complete permutation polynomials. (English) Zbl 1398.05012
Summary: 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 \(m\geq 2\). 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.

05A05 Permutations, words, matrices
11T06 Polynomials over finite fields
11T55 Arithmetic theory of polynomial rings over finite fields
Full Text: DOI
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