Abstract
We present a new method for constructing affine families of complex Hadamard matrices in every even dimension. This method has an intersection with Diţă’s construction and generalizes Szöllősi's method. We extend some known families and present new ones existing in even dimensions. In particular, we find more than 13 millon inequivalent affine families in dimension 32. We also find analytical restrictions for any set of four mutually unbiased bases existing in dimension six and for any family of complex Hadamard matrices existing in every odd dimension.
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