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.

翻译：在本文中,我们引入了一套可以用于McEliece加密系统的代码,称为Goppa类AG代码。这些代码概括了古典的Goppa代码,并且可以用任何genus $\ mathfrak{g}\geq $0的曲线来构建。我们关注了$C<unk> a,b}$的代码,我们研究了其双曲线的方形,以确定其是否抵制与Mora和Tillich开发的偏差和Goppa代码相似的区别攻击。我们还建议进行数字实验,以测量我们的界限有多清晰。</s>