APN functions in odd characteristic Original Research Article

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).