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：本文介绍了一类可用于McEliece密码系统的码族，称为类似Goppa的AG码。这些码推广了经典Goppa码，可从任意亏格$\mathfrak{g} \geq 0$的曲线构造得到。我们专注于$C_{a,b}$曲线上的码，研究其对偶平方维度的行为，以判定其抵御类似Mora和Tillich针对交错码与Goppa码所提出的区分攻击的能力。同时，我们还提出数值实验来评估所得界值的紧致程度。