A two-parameter family of complex Hadamard matrices of order 6 induced by hypocycloids

Szöllősi, Ferenc

doi:10.1090/S0002-9939-09-10102-8

A two-parameter family of complex Hadamard matrices of order $6$ induced by hypocycloids
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Proc. Amer. Math. Soc. 138 (2010), 921-928 Request permission

Abstract:

We construct a $2$-parameter family of complex Hadamard matrices of order $6$ by a natural block construction. We combine this family with an earlier result of Zauner to derive a $2$-parameter family of triplets of mutually unbiased bases (MUBs) in $\mathbb C^6$. This invalidates some numerical evidence given by Brierley and Weigert and sheds new light on the problem of determining the maximal number of MUBs in $\mathbb C^6$.

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