In this paper, we study the behavior of the true dimension of the subfield subcodes of Hermitian codes. Our motivation is to use these classes of linear codes to improve the parameters of the McEliece cryptosystem, such that key size and security level. The McEliece scheme is one of the promising alternative cryptographic schemes to the current public key schemes since in the last four decades, they resisted all known quantum computing attacks. By analyzing computational data series of true dimension, we concluded that they can be estimated by the extreme value distribution function.