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Explicit classes of permutation polynomials of \(\mathbb F_{3^{3m}}\). (English) Zbl 1215.11113
Summary: Permutation polynomials have been an interesting subject of study for a long time and have applications in many areas of mathematics and engineering. However, only a small number of specific classes of permutation polynomials are known so far. In this paper, six classes of linearized permutation polynomials and six classes of nonlinearized permutation polynomials over \(\mathbb{F}_{3^{3m}}\) are presented. These polynomials have simple shapes, and they are related to planar functions.

MSC:
11T06 Polynomials over finite fields
12E10 Special polynomials in general fields
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