Construction of Cartesian authentication codes from unitary geometry

In the present paper several constructions of Cartesian authentication codes from unitary geometry over finite fields are presented and their size parameters are computed. Assuming that the encoding rules are chosen according to a uniform probability distribution, the probabilities P _I and P _S of a successful impersonation attack and a successful substitution attack, respectively, of these codes are also computed. Moreover, those codes so constructed, for which P _I and P _S are nearly optimal, are also determined.