Vortex beams carrying orbital angular momentum (OAM), which featuring helical phase front, have been regarded as an alternative spatial degree of freedom for optical mode coding and multiplexing. For most reported OAM-based mode coding schemes, data information is only encoded by different OAM mode states. In this paper, we introduce a novel design technique to construct vortex array phase grating (VAPGs) for the flexible generation of vortex arrays, and employ the proposed VAPGs to realize multi-dimensional space/mode/amplitude coding/decoding. By designing VAPGs with different parameters and loading them on to a single spatial light modulator (SLM), we successfully generate vortex array with different mode states and relative power in the experiments. Moreover, a 10-bit multi-dimensional space/mode/amplitude data coding/decoding scheme for image transfer in free-space link with a zero bit-error-rate is experimentally demonstrated, which confirm the feasibility of our proposed VAPG-based coding/decoding scheme.