New bounds and constructions for authentication/secrecy codes with splitting

We investigate authentication codes with splitting, using the mathematical model introduced by Simmons. Besides an overview of the existing bounds, we obtain some new bounds for the probability of deception of the transmitter/ receiver in case of an impersonation or substitution game. We also prove some new bounds for a "spoofing attack of order L." Further, we give several new constructions for authentication/secrecy codes with splitting, derived from finite incidence structures such as partial geometries and affine resolvable designs. In some of these codes the bounds are attained with equality.