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Constructing permutations and complete permutations over finite fields via subfield-valued polynomials. (English) Zbl 1320.11123
Summary: We describe a recursive construction of permutation and complete permutation polynomials over a finite field \(\mathbb{F}_{p^n}\) by using \(\mathbb{F}_{p^k}\)-valued polynomials for several same or different factors \(k\) of \(n\). As a result, we obtain some specific permutation polynomials which unify and generalize several previous constructions.

MSC:
11T06 Polynomials over finite fields
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