Two new constructions of Cartesian authentication codes from symplectic geometry (Q1906578)

\textit{Z. Wan} [Des. Codes Cryptography 2, 333-356 (1992; Zbl 0764.94022)] used symplectic and unitary geometry over finite fields to construct Cartesian authentication codes and got some beautiful results. In the present paper, two new constructions of Cartesian authentication codes from symplectic geometry are presented and their size parameters are computed. Moreover, assume that the encoding rules are chosen according to a uniform probability distribution, the largest probabilities of a successful impersonation attack and of a successful substitution attack of these codes are also computed.