# zbMATH — the first resource for mathematics

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
##### Keywords:
finite fields; permutation polynomials; Kloosterman sums
Full Text:
##### References:
 [1] Ball, S.; Zieve, M., Symplectic spreads and permutation polynomials, (), 79-88 · Zbl 1066.51005 [2] A. Blokhuis, R.S. Coulter, M. Henderson, C.M. O’Keefe, Permutations amongst the Dembowski-Ostrom polynomials, in: D. Jungnickel, H. Niederreiter (Eds.), Finite Fields and Applications: Proceedings of the Fifth International Conference on Finite Fields and Applications, 2001, pp. 37-42 · Zbl 1009.11064 [3] Cohen, S.D., Permutation group theory and permutation polynomials, (), 133-146 · Zbl 0958.12001 [4] C.J. Corrada Bravo, P.V. Kumar, Permutation polynomials for interleavers in turbo codes, in: Proceedings of the IEEE International Symposium on Information Theory, Yokohama, Japan, June 29-July 4, 2003, p. 318 [5] Coulter, R.S., On the equivalence of a class of Weil sums in characteristic 2, New Zealand J. math., 28, 171-184, (1999) · Zbl 0979.11055 [6] Dobbertin, H., Uniformly representable permutation polynomials, (), 1-22 · Zbl 1041.11081 [7] Helleseth, T.; Zinoviev, V., New Kloosterman sums identities over $$\mathbb{F}_{2^m}$$ for all m, Finite fields appl., 9, 187-193, (2003) · Zbl 1081.11077 [8] Hirschfeld, J.W.P.; Storme, L., The packing problem in statistics, coding theory and finite projective spaces: update 2001, (), 201-246 · Zbl 1025.51012 [9] Hollmann, H.D.; Xiang, Q., A class of permutation polynomials of $$\mathbb{F}_{2^m}$$ related to dickson polynomials, Finite fields appl., 11, 1, 111-122, (2005) · Zbl 1073.11074 [10] Lidl, R.; Niederreiter, H., Finite fields, Encyclopedia math. appl., vol. 20, (1997), Cambridge Univ. Press Cambridge [11] Mullen, G.L., Permutation polynomials over finite fields, (), 131-151 · Zbl 0808.11069 [12] Sun, J.; Takeshita, O.Y., Interleavers for turbo codes using permutation polynomials over integer rings, IEEE trans. inform. theory, 51, 1, 101-119, (2005) · Zbl 1280.94121 [13] Sun, Q.; Wan, D., Permutation polynomials and their applications, (1987), Liaoning Education Press Shengyang, (in Chinese)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.