The quaternary complex Hadamard matrices of orders 10, 12, and 14

A complete classification of quaternary complex Hadamard matrices of orders 10, 12 and 14 is given, and a new parametrization scheme for obtaining new examples of affine parametric families of complex Hadamard matrices is provided. On the one hand, it is proven that all 10×10 and 12×12 quaternary complex Hadamard matrices belong to some parametric family, but on the other hand, it is shown by exhibiting an isolated 14×14 matrix that there cannot be a general method for introducing parameters into these types of matrices.