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In this paper, we introduce a family of codes that can be used in a McEliececryptosystem, called Goppa--like AG codes. These codes generalize classicalGoppa codes and can be constructed from any curve of genus $\mathfrak{g} \geq0$. Focusing on codes from $C_{a,b}$ curves, we study the behaviour of thedimension of the square of their dual to determine their resistance todistinguisher attacks similar to the one for alternant and Goppa codesdeveloped by Mora and Tillich. We also propose numerical experiments to measurehow sharp is our bound.

Goppa-like AG codes from $C_{a,b}$ curves and their behaviour under squaring their dual