Some Results on Bent-Negabent Boolean Functions over Finite Fields

We consider negabent Boolean functions that have Trace representation. We completely characterize quadratic negabent monomial functions. We show the relation between negabent functions and bent functions via a quadratic function. Using this characterization, we give infinite classes of bent-negabent Boolean functions over the finite field $\F_{2^n}$, with the maximum possible degree, $n \over 2$. These are the first ever constructions of negabent functions with trace representation that have optimal degree.