An Alternate Characterization of the Bentness of BinaryFunctions, with Uniqueness

Authors:
Claude Carlet;Philippe Guillot
Affiliations:
INRIA Projet CODES, Domaine de Voluceau, BP 105, 78153 Le Chesnay Cedex, France and GREYC, Université de Caen, France;Thomson-CSF Communication, 66 rue du Fossé blanc, 92231 Gennevilliers Cedex, France
Venue:
Designs, Codes and Cryptography
Year:
1998

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Abstract

In a previous paper, we have obtained a characterization of thebinary bent functions on (GF(2))^n (n even) as linearcombinations modulo 2^n/2, with integral coefficients, ofcharacteristic functions (indicators) of n/2-dimensional vector-subspaces of(GF(2))^n. There is no uniqueness of the representation of agiven bent function related to this characterization. We obtain now a newcharacterization for which there is uniqueness of the representation.