Recent studies of the distribution and kinematics of the Milky Way and Andromeda satellite galaxy systems have confirmed the existence of coplanar, corotating structures of galaxies. In addition to the ``missing satellite problem'', these structures pose a major challenge to the standard ΛCDM scenario of structure formation. We complement the efforts made by the dwarf galaxy community to extend these studies to other nearby galaxy groups by systematically searching for faint unresolved dwarf members with a low surface brightness in the Southern Centaurus group of galaxies. The aim is to determine whether these coplanar, corotating structures are a universal phenomenon. We imaged an area of 60sq.deg (0.3Mpc2) around the M83 subgroup with the wide-field Dark Energy Camera (DECam) at the CTIO 4m Blanco telescope in g and r down to a limiting surface brightness of µr≃30mag/arcsec2. Various image-filtering techniques were applied to the DECam data to enhance the visibility of extremely low-surface brightness objects. We report the discovery of 16 new dwarf galaxy candidates in the direction of the M83 subgroup, roughly doubling the number of known dwarfs in that region. The photometric properties of the candidates, when compared to those of the Local Group, suggest membership in the M83 subgroup. The faintest objects have a central star density of ≃1.3L☉/pc2 and a total magnitude of g=20.25, corresponding to Mg=-9.55 at the nominal distance of 4.9Mpc. The sky distribution of the new objects is significantly prolonged toward Cen A, suggesting that many of them belong to the Cen A subgroup or a common halo. We also provide updated surface photometry for the brighter, known dwarf members in the surveyed area. Modern survey CCD cameras and sophisticated detection algorithms can be used to systematically probe the faint end of the galaxy luminosity function around the M83 subgroup of galaxies. We aim at finding more and fainter members over a larger area to obtain a complete picture of the satellite galaxy substructure in the Centaurus group down to a total magnitude limit of MV≃-10.