On twin prime power Hadamard matrices
In this paper, we show that exactly one Hadamard matrix constructed using the twin prime power method is cocyclic. We achieve this by showing that the action of the automorphism group of a Hadamard matrix developed from a difference set induces a 2-transitive action on the rows of the matrix or is intransitive. We then use Itos classification of Hadamard matrices with 2-transitive automorphism groups to derive a necessary condition on the order of a cocyclic Hadamard matrix developed from a difference set. This work answers a research problem posed by K.J. Horadam, and exhibits the first known infinite family of Hadamard matrices which are not cocyclic.
twin prime powers hadamard matrix cocyclic 2-transitive action primary 05b20 05e18 secondary 20b20