Factoring \((16, 6, 2)\) Hadamard difference sets (Q1010845)

Summary: We describe a ``factoring'' method which constructs all twenty-seven Hadamard \((16,6,2)\) difference sets. The method involves identifying perfect ternary arrays of energy 4 (PTA(4)) in homomorphic images of a group \(G\), studying the image of difference sets under such homomorphisms and using the preimages of the PTA(4)s to find the ``factors'' of difference sets in \(G\). This ``factoring'' technique generalizes to other parameters, offering a general mechanism for creating Hadamard difference sets.