Abstract: In the present paper, we compute the number of the symplectic involutions over the finite field F with charF = 2, and also one Cartesian authentication code is obtained. Furthermore, its size parameters are computed completely. If assume that the coding rules are chosen according to a uniform probability, PI and PS denote the largest probabilities of a successful impersonation attack and a successful substitution attack respectively, then PI and PS are also computed.

Key words: authentication code, symplectic involution, finite field