The integrated modulation of radiation and scattering provides an unprecedented opportunity to reduce the number of electromagnetic (EM) apertures in the platform while simultaneously enhancing communication and stealth performance. Nevertheless, achieving full-polarization, arbitrary amplitude, and phase modulation of radiation scattering remains a challenge. In this paper, a strategy that realizes space-time coding of radiation scattering within the same frequency band, which enables the simultaneous and independent modulation of amplitude and phase, is proposed. To address the limitations of the high sideband levels (SBLs) of conventional space-time-coding metasurfaces, a strategy comprising nonuniform modulation periods and stochastic coding is proposed. Consequently, beam scanning with ultra-low sidelobe levels (SLLs) and suppressed SBLs is achieved in the radiation mode (RM). In scattering mode (SM), in-band low scattering characteristics are achieved within the same operating frequency band as RM. A prototype of a space-time-coding radiation-scattering metasurface (STCRSM) is fabricated and the aforementioned functionalities are validated by measurements. Furthermore, the proposed strategy does not necessitate the utilization of optimization algorithms and exhibits low SLLs and low SBLs, which will make it flourish in RF stealth applications, such as covert communication systems.