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The compositional inverse of a class of permutation polynomials over a finite field. (English) Zbl 1023.11061
Let $$q$$ be a power of $$2$$ and $$n$$ be an odd positive integer. Denote the trace mapping from $${\mathbb F}_{q^n}$$ to $${\mathbb F}_q$$ by $$\text{Tr}(X) = \sum_{i=0}^{n-1}X^{q^i}$$. Then as it has been shown in A. Blokhuis, R. Coulter, M. Henderson, and C. O’Keefe [Finite fields and applications V, Augsburg, 1999, 37-42 (2001; Zbl 1009.11064)] that the polynomial $f_\alpha(X) = X\operatorname {Tr}(X) + (\alpha+1)X^2$ induces a permutation of $${\mathbb F}_{q^n}$$ for any $$\alpha \in {\mathbb F}_q\setminus\{0,1\}$$. The authors provide formulas describing a polynomial $$g_\alpha(X)$$ which induces the inverse permutation.

##### MSC:
 11T06 Polynomials over finite fields 12E10 Special polynomials in general fields
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##### References:
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