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

AbstractIn a previous paper, we have obtained a characterization of the binary bent functions on (GF(2))n (n even) as linear combinations modulo $$2^{\frac{n}{2}}$$ , with integral coefficients, of characteristic functions (indicators) of $$\frac{n}{2}$$ -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.