标题： 一种新的编码理论，用于正常曲面和ADE奇点，I 显示英文标题

标题： A new coding theory, for normal surfaces, and ADE singularities, I

摘要： 在本文中，我们将与射影节点曲面相关的二进制码（严格码$\mathcal{K}$和扩展码$\mathcal{K}'$）的理论，扩展到正常曲面的编码理论，特别关注具有 ADE（有理双点）奇点的曲面。 我们定义了一种新的广义标记码理论，在几何情况下建立了这些码的权重的基本限制以及一些基本不等式。 我们建立的一个关键方法是将“码缩短”的概念扩展到广义码的情况：这是奇异点部分平滑的几何概念的代数对应物，并导致了祖先的概念，我们通过几个例子进行了说明。 显示英文摘要

摘要： In this article we extend the theory of the binary codes (the strict code $\mathcal{K}$ and the extended code $\mathcal{K}'$), associated to a projective nodal surface, to a coding theory for normal surfaces, with special consideration of the surfaces with ADE (Rational Double Points) singularities. We define a new theory of generalized labeled codes, establish in the geometric case basic restrictions for the weights of these codes, and some basic inequality. A crucial method that we establish is the extension of the concept of `code shortening' to the case of generalized codes: this is the algebraic counterpart of the geometric notion of a partial smoothing of the singular points, and leads to the concept of ancestors, which we illustrate through several examples.