Cocyclic Hadamard matrices from forms over finite Frobenius rings (Q1006025)

The authors give a construction of cocyclic Butson-Hadamard matrices. Their approach is based upon a finite Frobenius ring \(A\), a left \(A\)-module \(L\), a right \(A\)-module \(R\), and a bilinear pairing \(B:L\times R \to A\). Two such matrices (possibly from different rings) are equivalent if and only if the additive groups of the underlying right modules are isomorphic.