Disclosed is a mobile data carrier (M10-M40) or a read-write unit (L10-L40), comprising an antenna array (M11-M41; L11-L41) for the contactless exchange of data. According to the invention, means are provided for adjusting selected characteristics of the antenna array, the respective antenna array being provided with a directional diagram (M12-M41; L12-L42) having at least one maximum intensity of the received field strength. Said maximum intensities can then be adjusted, e.g. in the mobile data carriers, in such a way that the directional diagrams are focused on the read-write units positioned at the edge of a transport device (10), for example. This allows the lobes of the received field strength of the mobile data carriers to overlap to a great degree with the preferably also lobe-shaped directional diagrams of the received or transmitted field strengths of the read-write units when the mobile data carriers pass the read-write units, the directional diagrams of the received or transmitted field strengths of said read-write units extending all the way to the surface of the transport device.