In this paper, we design space-time block codes (STBCs) to broadcast the common information omnidirectionally in a massive multiple-input multiple-output downlink. To reduce the burden of the downlink channel estimation and achieve partial spatial diversity from base station (BS) transmit antennas, we propose channel-independently precoded low-dimensional STBC. The precoding matrix and the signal constellation in the low-dimensional STBC are jointly designed to guarantee omnidirectional coverage at any instant time and sufficiently utilize the power amplifier capacities of BS transmit antennas, and at the same time, achieve the full diversity of the low-dimensional STBC. Under this framework, several designs are presented. To provide transmit diversity order of two, a precoded Alamouti code is proposed, which has a fast symbolwise maximum-likelihood (ML) decoding. To provide transmit diversity order of four, a precoded quasi-orthogonal STBC is proposed, which has a pairwise ML decoding. Moreover, a precoded no-zero-entry Toeplitz code and a precoded no-zero-entry overlapped Alamouti code are also proposed. These two codes can achieve a higher diversity order with linear receivers.