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Permutation polynomials of the form $$(x^{p^m} - x + \delta)^s + L(x)$$ over the finite field $$\mathbb{F}_{p^{2 m}}$$ of odd characteristic. (English) Zbl 1315.05008
Summary: In this paper, we propose several classes of permutation polynomials with the form $$(x^{p^m} - x + \delta)^s + L(x)$$ over the finite field $$\mathbb{F}_{p^{2 m}}$$, where $$p$$ is an odd prime, and $$L(x)$$ is a linearized polynomial with coefficients in $$\mathbb{F}_p$$. The main method used in this paper is to determine the number of solutions of some equations over finite fields of odd characteristic.

MSC:
 11T06 Polynomials over finite fields
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References:
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