Codes over M2(F2) and applications to Golden space-time coded modulation

In this paper, we study code constructions over the finite ring M<inf>2</inf>(F<inf>2</inf>), the ring of 2×2 matrices with coefficients in the finite field F<inf>2</inf>. We show how they can be related to classical codes over F<inf>4</inf>. We provide as application the design of outer codes for 2 × 2 space-time coded modulation, when the inner code is the so-called Golden code.