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：本文提出了一类可应用于McEliece密码系统的码，称为类Goppa AG码。该类码推广了经典Goppa码，可从任意亏格$\mathfrak{g} \geq 0$的曲线构造。聚焦于来自$C_{a,b}$曲线的码，我们研究其对偶平方的维数性态，以确定其抵抗类似于Mora和Tillich针对交替码与Goppa码所提出的区分攻击的能力。我们还通过数值实验评估所给界的紧致程度。