Cocyclic Hadamard matrices and difference sets
This paper locates cocyclic Hadamard matrices within the mainstream of combinatorial design theory. We prove that the existence of a cocyclic Hadamard matrix of order 4t is equivalent to the existence of a normal relative difference set with parameters (4t,2,4t,2t) . In the basic case we note there is a corresponding equivalence between coboundary Hadamard matrices and MenonHadamard difference sets. These equivalences unify and explain results in the theories of Hadamard groups, divisible designs with regular automorphism groups, and periodic autocorrelation functions.
primary 05b20 secondary 05b05 05b10 20j06