  Hypergraph states as real equally weighted pure states are important
resources for quantum codes of non-local stabilizer. Using local Pauli
equivalence and permutational symmetry, we reduce the 32768 four qubit real
equally weighted pure states to 28 locally inequivalent hypergraph states and
several graph states. The calculation of geometric entanglement supplemented
with entanglement entropy confirms that further reduction is impossible for
true hypergraph states.
