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Specific permutation polynomials over finite fields. (English) Zbl 1261.11080
Summary: We present new classes of permutation polynomials over finite fields. If $$q$$ is the order of the finite field, some of these polynomials have the form $$x^rf(x^{(q-1)/d})$$, where $$d\mid (q-1)$$. We also present some permutation polynomials involving the trace function, which plays an additive role analogous to $$x^{(q-1)/d}$$. Finally, we present a generalization involving other symmetric functions of $$x,x^p,\cdots ,x^{q/p}$$.

##### MSC:
 11T06 Polynomials over finite fields
##### Keywords:
finite field; permutation polynomial; complete mapping
Full Text:
##### References:
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