Bracken, Carl and Byrne, Eimear and Markin, Nadya and McGuire, Gary
Fourier Spectra of Binomial APN Functions.
Siam Journal on Discrete Mathematics, 23 (2).
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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