Media-based modulation (MBM), which utilizes radiation patterns of a reconfigurable antenna to convey information, appears as a promising index modulation (IM) scheme for beyond 5G networking. In this paper, we present a general framework for MBM from the perspective of space-time coding, and introduce a novel space-time coded IM concept, which is called space-time media-based modulation (ST-MBM). The proposed scheme is based on one of the prominent IM solutions, space shift keying, along with Hurwitz-Radon family of matrices in order to achieve transmit diversity gain with a single radio frequency (RF) chain by utilizing the unique RF mirror activation principle of MBM. We derive the theoretical pair wise error probability of the ST-MBM scheme for correlated and uncorrelated channel states and obtain the average bit error probability. Additionally, a lower bound is derived for the mutual information of the ST-MBM scheme to gain insights into the information theoretical bounds of the proposed scheme.