In this paper a construction of quantum codes from self-orthogonal algebraic geometry codes is provided. Our method is based on the CSS construction as well as on some peculiar properties of the underlying algebraic curves, named Swiss curves. Several classes of well-known algebraic curves with many rational points turn out to be Swiss curves. Examples are given by Castle curves, GK curves, generalized GK curves and the Abdón–Bezerra–Quoos maximal curves. Applications of our method to these curves are provided. Our construction extends a previous one due to Hernando, McGuire, Monserrat, and Moyano-Fernández.

中文翻译：

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关于某些自正交AG码及其在量子纠错码中的应用

本文提供了一种由自正交代数几何代码构成的量子代码。我们的方法基于CSS构造以及基础代数曲线（称为Swiss曲线）的某些特殊属性。几类具有许多有理点的著名代数曲线证明是瑞士曲线。城堡曲线，GK曲线，广义GK曲线和Abdón–Bezerra–Quoos最大曲线给出了示例。提供了我们的方法在这些曲线上的应用。由于Hernando，McGuire，Monserrat和Moyano-Fernández，我们的建筑得到了扩展。