Extension of the Set of Complex Hadamard Matrices of Size 8

A complex Hadamard matrix is defined as a matrix H which fulfills two conditions, $$|H_{j,k}|=1$$|Hj,k|=1 for all j and k and $$HH^{*}=N \mathbb {I}_N$$HH∗=NIN where $$\mathbb {I}_N$$IN is an identity matrix of size N. We explore the set of complex Hadamard matrices $$\mathcal {H}_N$$HN of size $$N=8$$N=8 and present two previously unknown structures: a one-parametric, non-affine family $$T_8^{(1)}$$T8(1) of complex Hadamard matrices and a single symmetric and isolated matrix $$A_8^{(0)}$$A8(0).

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