An Alternate Characterization of the Bentness of Binary Functions, with Uniqueness

In a previous paper, we have obtained a characterization of the binary bent functions on (GF(2))ⁿ (n even) as linear combinations modulo , with integral coefficients, of characteristic functions (indicators) of -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.