The connection between quadratic bent–negabent functions and the Kerdock code

In this paper we prove that all bent functions in the Kerdock code, except for the coset of the symmetric quadratic bent function, are bent–negabent. In this direction, we characterize the set of quadratic bent–negabent functions and show some results connecting quadratic bent–negabent functions and the Kerdock code. Further, we note that there are bent–negabent preserving nonsingular transformations outside the well known class of orthogonal ones that might provide additional functions in the bent–negabent set. This is the first time we could identify non-orthogonal (nonsingular) linear transformations that preserve bent–negabent property for a special subset.