Fourier Spectra of Binomial APN Functions
Bracken, Carl and Byrne, Eimear and Markin, Nadya and McGuire, Gary (2009) Fourier Spectra of Binomial APN Functions. Siam Journal on Discrete Mathematics, 23 (2). pp. 596-608. ISSN 0895-4801
In this paper we compute the Fourier spectra of some recently discovered binomial APN functions. One consequence of this is the determination of the nonlinearity of the functions, which measures their resistance to linear cryptanalysis. Another consequence is that certain error-correcting codes related to these functions have the same weight distribution as the 2-error-correcting BCH code. Furthermore, for field extensions of F2 of odd degree, our results provide an alternative proof of the APN property of the functions.
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