On the Fourier Spectra of the Infinite Families of Quadratic APN Functions
Bracken, Carl and Zha, Zhengbang (2009) On the Fourier Spectra of the Infinite Families of Quadratic APN Functions. Advances in Mathematics of Communications , 3 (3). pp. 219-226. ISSN 1930-5346
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 new quadranomial family of APN functions. With this result, all known infinite families of APN functions now have their Fourier spectra and hence their nonlinearities computed.
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