  The main of this paper is to prove that in terms of normalized density, a
space-time block code based on an irreducible quadratic polynomial over the
Eisenstein integers is an optimal space-time block code compared with any
quadratic space-time block code over the ring of integers of imaginary
quadratic fields. In addition we find the optimal design of space-time block
codes based on an irreducible quadratic polynomial over some rings of imaginary
quadratic fields.
