In this paper we prove two general characterization theorems for A-codes, that provide r-fold security, in terms of well-known combinatorial structures (t-designs and orthogonal arrays). We use Delsarte's linear programming method to find new bounds on the number of encoding rules for Cartesian A-codes with 1-fold and 2-folds security and show that in the latter case the bound is achieved by A-codes obtained from the dual of two well-studied error correcting codes: an MDS code and the extended Hamming code.