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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 \(\mathbb{Z}^{2t}_2\).

94A60 Cryptography
94C10 Switching theory, application of Boolean algebra; Boolean functions (MSC2010)
06E30 Boolean functions
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