Conjecture on the nonexistence of homogeneous rotation symmetric bent functions

A Boolean function is homogeneous if all its monomials have the same degree, and rotation symmetric if it is invariant under cyclic permutations of its variables. A Boolean function is bent when it has maximal distance from the affine Boolean functions. The degree of a Boolean function is its algebraic degree. Nonexistence conjecture. There are no homogeneous rotation symmetric bent functions of degree $>2$. This conjecture was proposed after exhaustive searches found no homogeneous rotation symmetric bent functions of degrees $3$, $4$, or $5$ in $10$ variables. The paper presents results supporting it, but the conjecture remains open in the supplied source.