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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
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