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A recursive construction of permutation polynomials over $$\mathbb F_{q^2}$$ with odd characteristic related to Rédei functions. (English) Zbl 1445.11141
Summary: In this paper, we construct two classes of permutation polynomials over $$\mathbb F_{q^2}$$ with odd characteristic closely related to rational Rédei functions. Two distinct characterizations of their compositional inverses are also obtained. These permutation polynomials can be generated recursively. As a consequence, we can generate permutation polynomials with an arbitrary number of terms in a very simple way. Moreover, several classes of permutation binomials and trinomials are given. With the help of a computer, we find that the number of permutation polynomials of these types is quite big.

##### MSC:
 11T06 Polynomials over finite fields
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##### References:
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