On Construction of Optimal A2-Codes

Two authentication codes with arbitration (A^2-codes) are constructed from finite affine spaces to illustrate for the first time that the information-theoretic lower bounds for A^2-eodes can be strictly tighter than the combinatorial ones. The codes also illustrate that the conditional combinatorial lower bounds on numbers of encoding\ decoding rules are not genuine ones. As an analogue of 3-dimensional ease, an A2-code from ,*-dimensional finite projective spaces is construeted, which meets both the information-theoretic and combinatorial lower bounds.