关于某些self-orthogonal AG码及其在量子纠错码中的应用
On certain self-orthogonal AG codes with applications to Quantum error-correcting codes
摘要：
本文利用自正交代数几何码构造量子码。我们的方法是基于CSS建设以及对一些特殊性质的基础代数曲线，瑞士曲线。几类著名的具有许多有理点的代数曲线都是瑞士曲线。以Castle曲线、GK曲线、广义GK曲线和Abdon-Bezerra-Quoos极大曲线为例。我们的方法，这些曲线的应用程序。我们的建设扩展了以前的一个由于赫尔南多，麦圭尔，蒙特塞拉特和莫亚诺费尔南德斯。
英文摘要：
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 Abdon-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-Fernandez.
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