An alternate characterization of the bentness of binary functions, with uniqueness

Claude Carlet

GREYC, UniversitÚ de Caen
BP 105
78153 Le Chesnay Cedex, France

Philippe Guillot
Thomson-CSF Communication
66 rue du FossÚ blanc
92231 Gennevilliers Cedex, France.

Designs, Codes and Cryptography, 14(2): 133-140, 1998.


In a previous paper, we have obtained a characterization of the binary bent functions on GF(2)n (n even) as linear combinations modulo 2n/2, with integral coefficients, of characteristic functions (indicators) of n/2-dimensional vector-subspaces of GF(2)n. There is no uniqueness of the representation of a given bent function related to this characterization. We obtain now a new characterization for which there is uniqueness of the representation.