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Permutation polynomials of the \((x^p - x+\delta)^s+L(x)\). (English) Zbl 1211.11136
In this article the authors prove the equivalence of Kloosterman polynomials of the form \(L_{1,d}\) and permutation polynomials of the form \((x^p -x + \delta )^s + L(x)\) over finite fields \(\mathbb F_{p^m}\) and where \(L(x)\) is a linearized polynomial with coefficients in the finite field \(\mathbb F_p\). They present six classes of permutation polynomials over \(\mathbb F_{2^m}\) of the form \((x^2 +x + \delta )^s + L_c(x)\). Moreover, they describe three classes of permutation polynomials of similar forms over the finite field \(\mathbb F_{3^m}\).

MSC:
11T06 Polynomials over finite fields
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[1] Coulter, R.S., On the evaluation of a class of Weil sums in characteristic 2, New Zealand J. math., 28, 171-184, (1999) · Zbl 0979.11055
[2] 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
[3] Hollmann, H.D.L.; Xiang, Q., Kloosterman sum identities over \(\mathbb{F}_{2^m}\), Discrete math., 279, 277-286, (2004) · Zbl 1099.11040
[4] 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
[5] Lidl, R.; Mullen, G.L.; Turnwald, G., Dickson polynomials, (1993), Longman · Zbl 0823.11070
[6] Lidl, R.; Niederreiter, H., Finite fields, Encyclopedia math. appl., vol. 20, (1997), Cambridge Univ. Press Cambridge
[7] Yuan, J.; Ding, C., Four classes of permutation polynomials of \(\mathbb{F}_{2^m}\), Finite fields appl., 13, 4, 869-876, (2007) · Zbl 1167.11045
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