Properties and constructions of coincident functions

Morgan Barbier 1 Hayat Cheballah 1 Jean-Marie Le Bars 1
1 Equipe Monétique & Biométrie - Laboratoire GREYC - UMR6072
GREYC - Groupe de Recherche en Informatique, Image, Automatique et Instrumentation de Caen
Abstract : Extensive studies of Boolean functions are carried in many fields. The Mobius transform is often involved for these studies. In particular, it plays a central role in coincident functions, the class of Boolean functions invariant by this transformation. This class – which has been recently introduced – has interesting properties, in particular if we want to control both the Hamming weight and the degree. We propose an innovative way to handle the Mobius transform which allows the composition between several Boolean functions and the use of Shannon or Reed-Muller decompositions. Thus we benefit from a better knowledge of coin-cident functions and introduce new properties. We show experimentally that for many features, coincident functions look like any Boolean functions.
Type de document :
Pré-publication, Document de travail
2015
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Dernière modification le : mardi 5 juin 2018 - 10:14:40
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  • HAL Id : hal-01178356, version 1
  • ARXIV : 1507.05316

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Morgan Barbier, Hayat Cheballah, Jean-Marie Le Bars. Properties and constructions of coincident functions. 2015. 〈hal-01178356〉

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