  We propose a new class of space-time block codes based on finite-field
rank-metric codes in combination with a rank-metric-preserving mapping to the
set of Eisenstein integers. It is shown that these codes achieve maximum
diversity order and improve upon certain existing constructions. Moreover, we
present a new decoding algorithm for these codes which utilizes the algebraic
structure of the underlying finite-field rank-metric codes and employs
lattice-reduction-aided equalization. This decoder does not achieve the same
performance as the classical maximum-likelihood decoding methods, but has
polynomial complexity in the matrix dimension, making it usable for large field
sizes and numbers of antennas.
