  In this paper, we consider the problem of Mutually Unbiased Bases in prime
dimension $d$. It is known to provide exactly $d+1$ mutually unbiased bases. We
revisit this problem using a class of circulant $d \times d$ matrices. The
constructive proof of a set of $d+1$ mutually unbiased bases follows, together
with a set of properties of Gauss sums, and of bi-unimodular sequences.
