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Four classes of permutation polynomials of \(\mathbb F_{2^m}\). (English) Zbl 1167.11045
Summary: Permutation polynomials have been a subject of study for over 140 years and have applications in many areas of science and engineering. However, only a handful of specific classes of permutation polynomials are known so far. In this paper we describe four classes of permutation polynomials over \(\mathbb F_{2^m}\). Two of the four classes have the same form, while the other two classes are of different forms. Our work is motivated by a recent paper by T. Helleseth and V. Zinoviev [Finite Fields Appl. 9, No. 2, 187–193 (2003; Zbl 1081.11077)].

MSC:
11T06 Polynomials over finite fields
11L05 Gauss and Kloosterman sums; generalizations
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