  In this paper, we introduce a family of codes that can be used in a McEliece
cryptosystem, called Goppa--like AG codes. These codes generalize classical
Goppa codes and can be constructed from any curve of genus $\mathfrak{g} \geq
0$. Focusing on codes from $C_{a,b}$ curves, we study the behaviour of the
dimension of the square of their dual to determine their resistance to
distinguisher attacks similar to the one for alternant and Goppa codes
developed by Mora and Tillich. We also propose numerical experiments to measure
how sharp is our bound.
