Permutation polynomials of the \((x^p - x+\delta)^s+L(x)\). (English) Zbl 1211.11136

Yuan, Jin; Ding, Cunsheng; Wang, Huaxiong; Pieprzyk, Josef

Finite Fields Appl. 14, No. 2, 482-493 (2008).

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 \(\mathbb F_{3^m}\).

Reviewer: Jebrel M. Habeb (Irbid)

MSC:

11T06

Polynomials over finite fields

Keywords:

Permutation polynomials; Kloosterman polynomials

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