APN functions in odd characteristic

Authors:
Hans Dobbertin;Donald Mills;Eva Nuria Müller;Alexander Pott;Wolfgang Willems
Affiliations:
Faculty of Mathematics, Universitätsstrasse 150, D-44780 Bochum, Germany;Department of Mathematics, Southern Illinois University, Carbondale, IL;Institute for Algebra and Geometry, Otto-von-Guericke-University Magdeburg, D-39016 Magdeburg, Germany;Institute for Algebra and Geometry, Otto-von-Guericke-University Magdeburg, D-39016 Magdeburg, Germany;Institute for Algebra and Geometry, Otto-von-Guericke-University Magdeburg, D-39016 Magdeburg, Germany
Venue:
Discrete Mathematics - Special issue: Combinatorics 2000
Year:
2003

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Abstract

Recently, the investigation of so-called almost perfect nonlinear (APN) functions has attracted a lot of research interest. In particular, the case of even characteristic has been investigated. The notion of "APN" has been extended to the nonbinary case and several such mappings have been discovered. In this paper, we add some more examples. Our results explain some of the "open cases" in the tables of Helleseth et al. (IEEE Trans. Inform. Theory 45 (1999) 475).