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arXiv · 1604.02830

Decomposing generalized bent and hyperbent functions

Thor Martinsen·Wilfried Meidl·Sihem Mesnager·Pantelimon Stanica
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Abstract

In this paper we introduce generalized hyperbent functions from $F_{2^n}$ to $Z_{2^k}$, and investigate decompositions of generalized (hyper)bent functions. We show that generalized (hyper)bent functions from $F_{2^n}$ to $Z_{2^k}$ consist of components which are generalized (hyper)bent functions from $F_{2^n}$ to $Z_{2^{k^\prime}}$ for some $k^\prime < k$. For odd $n$, we show that the Boolean functions associated to a generalized bent function form an affine space of semibent functions. This complements a recent result for even $n$, where the associated Boolean functions are bent.

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Thor Martinsen, Wilfried Meidl, Sihem Mesnager, Pantelimon Stanica. 2016-04-11. Decomposing generalized bent and hyperbent functions. https://arxiv.org/abs/1604.02830

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