Real and complex unbiased Hadamard matrices
  We use combinatorial and Fourier analytic arguments to prove various non-existence results on systems of real and complex unbiased Hadamard matrices. In particular, we prove that a complete system of complex mutually unbiased Hadamard matrices (MUHs) in any dimension $d$ cannot contain more than one real Hadamard matrix. We also give new proofs of several known structural results in low dimensions, for $d\le 6$. 
Mate Matolcsi, Imre Z. Ruzsa, Mihaly Weiner
math.CO