GOB designs for authentication codes with arbitration

Combinatorial characterization of optimal authentication codes with arbitration was previously given by several groups of researchers in terms of affine a-resolvable $+$ BIBDs and $\alpha$-resolvable designs with some special properties, respectively. In this paper, we revisit this known characterization and restate it using a new idea of GOB designs. This newly introduced combinatorial structure simplifies the characterization , and enables us to extend Johansson's well-known family of optimal authentication codes with arbitration to any finite projective spaces with dimension greater than or equal to 3.