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摘要翻译：
Altmann、Hausen和Suess等人对低维环面作用下的完全正规变体进行了描述，推广了环面变体的理论。在作用环面T的余维为1的情况下，我们描述了T不变的Weil和Cartier因子，并给出了计算整体截面、交点数和Euler特征的公式。作为一个应用，我们利用这些所谓的T变体上的因子来定义新的评价码，称为T码。我们用交集理论求出了它们最小距离的估计值。这推广了toric码的理论，并将其与曲线上的AG码相结合。作为一般技术的最简单的应用，我们来看看来自可分解向量束的直纹面上的代码。这种构造已经给出了比相关产品代码更好的代码。进一步的例子表明，我们可以通过构造更复杂的T变体来改进这些代码。这些结果建议进一步寻找关于T变种的好代码。
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英文标题：
《AG Codes from Polyhedral Divisors》
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作者：
Nathan Ilten and Hendrik S\"u{\ss}
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最新提交年份：
2009
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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一级分类：Computer Science 计算机科学
二级分类：Information Theory 信息论
分类描述：Covers theoretical and experimental aspects of information theory and coding. Includes material in ACM Subject Class E.4 and intersects with H.1.1.
涵盖信息论和编码的理论和实验方面。包括ACM学科类E.4中的材料，并与H.1.1有交集。
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一级分类：Mathematics 数学
二级分类：Information Theory 信息论
分类描述：math.IT is an alias for cs.IT. Covers theoretical and experimental aspects of information theory and coding.
它是cs.it的别名。涵盖信息论和编码的理论和实验方面。
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英文摘要：
A description of complete normal varieties with lower dimensional torus action has been given by Altmann, Hausen, and Suess, generalizing the theory of toric varieties. Considering the case where the acting torus T has codimension one, we describe T-invariant Weil and Cartier divisors and provide formulae for calculating global sections, intersection numbers, and Euler characteristics. As an application, we use divisors on these so-called T-varieties to define new evaluation codes called T-codes. We find estimates on their minimum distance using intersection theory. This generalizes the theory of toric codes and combines it with AG codes on curves. As the simplest application of our general techniques we look at codes on ruled surfaces coming from decomposable vector bundles. Already this construction gives codes that are better than the related product code. Further examples show that we can improve these codes by constructing more sophisticated T-varieties. These results suggest to look further for good codes on T-varieties.
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PDF链接：
https://arxiv.org/pdf/0811.2696
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