There have been a lot of effort to construct good quantum codes from the classical error correcting codes. Constructing new quantum codes using Hermitian self-orthogonal codes seems to be a difficult problem in general. In this paper, Hermitian self-orthogonal codes are studied from algebraic function fields. Sufficient conditions for the Hermitian self-orthogonality of an algebraic geometry code are presented. New Hermitian self-orthogonal codes are constructed from projective lines, hyper-elliptic curves and Hermitian curves. As an application, new families of quantum stabilizer codes are provided. Additionally, six new families of MDS quantum codes are obtained.
翻译：从古典误差校正代码中构建良好的量子代码已经付出了大量努力。 使用埃米提亚自垂直代码构建新的量子代码在总体上似乎是一个困难的问题。 在本文中,从代数功能领域对埃米提亚自垂直代码进行了研究,为埃米提亚自垂直测距代码提供了充分的条件。 新的赫米提亚自垂直代码是从投射线、超椭圆曲线和赫米提曲线构建的。 作为应用,提供了量子稳定代码的新组合。 此外,还获得了六种新组合的MDS量子代码。
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