In the theory of communication, both coding and cryptology play an important role. They are algebraic theories closely related to combinatorics. t-designs are very important combinatorial structures which have well-known relationships with error-detecting and correcting codes. We will introduce the inclusion matrix of a combinatorial structure in order to emphasize the differences between multidesigns and extended designs. We prove that a full combinatorial multidesign exists and, moreover, we compute its parameters. © 1993.