Abstract

We present a new parametrization of families of complex Hadamard matrices stemming from the Fourier matrices in every prime power dimension. We connect continuous Abelian groups with families of complex Hadamard matrices and conjecture that the constructed families are maximal. Also, we derive new relations for complex Hadamard matrices in every prime power dimension and prove that some real Hadamard matrices can be written as a product of an arbitrarily large number of real Hadamard matrices.