Block-Circulant Complex Hadamard Matrices

A new method of obtaining a sequence of isolated complex Hadamard matrices (CHM) for dimensions $N\geqslant 7$, based on block-circulant structures, is presented. We discuss, several analytic examples resulting from a modification of the Sinkhorn algorithm. In particular, we present new isolated matrices of orders $9$, $10$ and $11$, which elements are not roots of unity, and also several new multiparametric families of order $10$. We note novel connections between certain eight-dimensional matrices and provide new insights towards classification of CHM for $N\geqslant 7$. These contributions can find real applications in Quantum Information Theory and constructions of new families of Mutually Unbiased Bases or Unitary Error Bases.