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On inverse permutation polynomials. (English) Zbl 1183.11075
Summary: We give an explicit formula of the inverse polynomial of a permutation polynomial of the form \(x^rf(x^s)\) over a finite field \(\mathbb F_q\) where \(s|q - 1\). This generalizes results in [A. Muratović-Ribić, Finite Fields Appl. 13, No. 4, 977–980 (2007; Zbl 1167.11044)] where \(s=1\) or \(f = g^{\frac{q-1}{s}}\) were considered respectively. We also apply our result to several interesting classes of permutation polynomials.

MSC:
11T06 Polynomials over finite fields
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