Quadratic permutations, complete mappings and mutually orthogonal latin squares

We investigate the permutation behavior of a special class of Dembowski-Ostrom polynomials over a finite field of characteristic 2 of the formOne of the newly identified classes contains a subclass of complete mappings. We use these complete mappings to define new sets of mutually orthogonal Latin squares, as well as new vectorial bent functions from the Maiorana-McFarland class. Moreover, the quasigroup polynomials obtained in the process are different and inequivalent to the previously known ones.