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On the coefficients of binary bent functions. (English) Zbl 0941.94016
A function $$f:\mathbb{Z}^m_2\to\mathbb{Z}_2$$ is called a bent function if the values of the Fourier transform of $$(-1)^f$$ are always $$\pm 1$$. Bent functions, which exist if and only if $$m$$ is even, play an important role in discrete mathematics though many applications in coding theory, design theory and cryptography. The present paper is an attempt in the direction of a better understanding of the fundamental structure of bent functions. The main result is a 2-adic inequality satisfied by the coefficients of bent functions in their polynomial representations. These identities also lead to the discovery of some new affine invariants of Boolean functions on $$\mathbb{Z}^{2t}_2$$.

##### MSC:
 94A60 Cryptography 94C10 Switching theory, application of Boolean algebra; Boolean functions (MSC2010) 06E30 Boolean functions
##### Keywords:
bent function; Boolean functions
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