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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.

##### MSC:
 05A05 Permutations, words, matrices 11T06 Polynomials over finite fields 11T55 Arithmetic theory of polynomial rings over finite fields
MISTY
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