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August  2009, 3(3): 219-226. doi: 10.3934/amc.2009.3.219

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

Carl Bracken 1, and  Zhengbang Zha 2,

1. 

Department of Mathematics, National University of Ireland Maynooth, Co. Kildare, Ireland
2. 

School of Mathematical Sciences, Luoyang Normal University, Luoyang 471022, China

Received  November 2008 Revised  July 2009 Published  August 2009

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 quadrinomial 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.
Keywords: APN function, nonlinearity., Fourier spectrum.
Mathematics Subject Classification: 11T23, 11T71, 94B0.
Citation: Carl Bracken, Zhengbang Zha. On the Fourier spectra of the infinite families of quadratic APN functions. Advances in Mathematics of Communications, 2009, 3 (3) : 219-226. doi: 10.3934/amc.2009.3.219
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