New Constructions of Group-Invariant Butson Hadamard Matrices

Let G be a finite group and let h positive integer. A BH(G, h) matrix is G-invariant ∣G∣ × H whose entries are complex hth roots of unity such that H* = ∣G∣I∣G∣, where denotes the conjugate transpose H, I∣G∣ identity order ∣G∣. In this paper, we give three new constructions matrices. The first construction known family matrices in which does not need to abelian. second third two families local ring.