代数几何码与低维Hull的线性码近40年来一直是研究的热门课题。许多具有良好性能的线性码都是由代数几何码构造的。代数几何码与低维Hull的线性码在秘密共享方案、量子码、以及渐近优码的构造方面都有重要的应用。本课题研究一些具有良好性能的代数几何码的构造方法以及利用这些码与其他一些工具构造具有低维Hull的线性码的新方法，分析这些码的代数与几何结构，最后利用这些码构造一些新参数的量子码与秘密共享方案。这些研究不仅在理论上具有重要意义，同时具有很好的应用前景。

Algebraic-geometry codes (AG-codes) and linear codes with low dimensional Hull are hot researching topics in recent 40 years. Many linear codes with good properties are constructed by using algebraic-geometry codes. AG-codes and linear codes with low dimensional Hull have many applications in security sharing schemes, quantum codes, and asymptotically good codes. This project is devoted to investigating the constructions of AG-codes with good properties and new approaches to obtaining linear codes with low dimensional Hull. Then we will analysis the algebraic and geometric structure of such codes. Finally, we will use these codes to get some quantum codes with new parameters and new security sharing schemes. This research not only has its great meaning on theory, and also has good application foreground.