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×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