Permutation polynomials of degree 6 or 7 over finite fields of characteristic 2

Authors:
Jiyou Li;David B. Chandler;Qing Xiang
Affiliations:
Mathematics Department, Shanghai JiaoTong University, Shanghai 200240, PR China;Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA;Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA
Venue:
Finite Fields and Their Applications
Year:
2010

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Abstract

In Dickson (1896-1897) [2], the author listed all permutation polynomials up to degree 5 over an arbitrary finite field, and all permutation polynomials of degree 6 over finite fields of odd characteristic. The classification of degree 6 permutation polynomials over finite fields of characteristic 2 was left incomplete. In this paper we complete the classification of permutation polynomials of degree 6 over finite fields of characteristic 2. In addition, all permutation polynomials of degree 7 over finite fields of characteristic 2 are classified.