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Permutation polynomials of the $$(x^p - x+\delta)^s+L(x)$$. (English) Zbl 1211.11136
In this article the authors prove the equivalence of Kloosterman polynomials of the form $$L_{1,d}$$ and permutation polynomials of the form $$(x^p -x + \delta )^s + L(x)$$ over finite fields $$\mathbb F_{p^m}$$ and where $$L(x)$$ is a linearized polynomial with coefficients in the finite field $$\mathbb F_p$$. They present six classes of permutation polynomials over $$\mathbb F_{2^m}$$ of the form $$(x^2 +x + \delta )^s + L_c(x)$$. Moreover, they describe three classes of permutation polynomials of similar forms over the finite field $$\mathbb F_{3^m}$$.

##### MSC:
 11T06 Polynomials over finite fields
##### Keywords:
Permutation polynomials; Kloosterman polynomials
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##### References:
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