Factoring (16, 6, 2) Hadamard Difference Sets - Bhattacharya, Chirashree; Smith, Ken W. (The Electronic Journal of Combinatorics, 2008)
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.