Enumeration of the bent functions of least deviation from a quadratic bent function

We study a construction of the bent functions of least deviation from a quadratic bent function, describe all these bent functions of 2k variables, and show that the quantity of them is 2 ^k (2¹ + 1) ... (2 ^k + 1). We find some lower bound on the number of the bent functions of least deviation from a bent function of the Maiorana-McFarland class.