On the Fourier spectra of the infinite families of quadratic APN functions

It is well known that a quadratic function defined on a finite field of 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 the values in the Fourier spectrum of a function and the APN property. In this article we compute the Fourier spectrum of the quadranomial family of APN functions from [5]. With this result, all known infinite families of APN functions now have their Fourier spectra and hence their nonlinearities computed.