On the Fourier spectra of the infinite families of quadratic APN functions
Carl Bracken, Zhengbang Zha · Advances in Mathematics of Communications · 2009
It is well known that a quadratic function defined on a finite fieldof odd degree is almost bent (AB) if and only if it is almost perfect nonlinear(APN). For the even degree case there is no apparent relationship between thevalues in the Fourier spectrum of a function and the APN property. In thisarticle we compute the Fourier spectrum of the quadrinomial family of APNfunctions from [5]. With this result, all known infinite families of APN functionsnow have their Fourier spectra and hence their nonlinearities computed.