Homogeneous Bent Functions

This paper discusses homogeneous bent functions. The space of homogeneous functions of degree three in six boolean variables was exhaustively searched and thirty bent functions were found. These are found to occur in a single orbit under the action of relabelling of the variables. The homogeneous bent functions identified exhibit interesting combinatorial structures and are, to the best of our knowledge, the first examples of bent functions without quadratic terms. A construction for other homogeneous bent functions of degree three in larger spaces is also given.