On the parametrization of classes of conjugate-normal Toeplitz matrices

The conjugate-normal Toeplitz problem is the one of characterizing matrices that are simultaneously Toeplitz and conjugate-normal. It is shown that the descriptions of all classes of conjugate-normal Toeplitz matrices can be regarded as constructive procedures. A parametrization is performed for each of the available classes; that is, a set of parameters is proposed whose values allow one to uniquely determine all the entries of a matrix belonging to this class.