平面曲线的符号Hamburger-Noether表达式与AG码的构造
Symbolic Hamburger-Noether expressions of plane curves and construction of AG codes
AI总结：
本文提出基于符号Hamburger-Noether表达式的算法，计算有理除子空间基和Weierstrass半群，用于代数几何码的构造与译码。
摘要：
我们提出一个算法，用于计算空间L(G)的基，其中G是定义在非奇异绝对不可约代数曲线上的有理除子；我们还提出另一个算法，用于计算点P处的Weierstrass半群，以及该半群中每个值对应的函数，其中P是曲线的一个奇异平面模型的有理分支。该方法基于Brill-Noether算法，通过适当结合Hamburger-Noether展开理论与虚拟通过条件的施加来实现。这些算法以符号计算的形式给出，引入了符号Hamburger-Noether表达式的概念。所有这些都可以应用于代数几何码的有效构造以及此类码的译码问题，包括Feng和Rao方案用于单点码的情形。
英文摘要：
We present an algorithm to compute bases for the spaces L(G), provided G is a rational divisor over a non-singular absolutely irreducible algebraic curve, and also another algorithm to compute the Weierstrass semigroup at P together with functions for each value in this semigroup, provided P is a rational branch of a singular plane model for the curve. The method is founded on the Brill-Noether algorithm by combining in a suitable way the theory of Hamburger-Noether expansions and the imposition of virtual passing conditions. Such algorithms are given in terms of symbolic computation by introducing the notion of symbolic Hamburger-Noether expressions. Everything can be applied to the effective construction of Algebraic Geometry codes and also in the decoding problem of such codes, including the case of the Feng and Rao scheme for one-point codes.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
