论文标题
向表面塔的良好代码家庭
Toward good families of codes from towers of surfaces
论文作者
论文摘要
我们在本文中介绍了一种新方法，以估计代码与代数表面的最小距离。该下限是通用的，即可以应用于任何表面，事实证明在有限的形态下是``提升''，为从表面塔楼构建良好代码的道路铺平了道路。在同一方向上，我们为具有固定有限的封闭积分$ \ Mathcal P $的表面标准建立了标准，以拥有$ \ ell $ - étale封面的无限塔，其中$ \ Mathcal p $完全分配。我们结束时说明了几个开放问题。特别是，我们将具有非常丰富的规范类别的一般类型表面的渐近代码与它们相对于其$ k^2 $的合理点的行为以及连贯的Euler特征联系起来。
We introduce in this article a new method to estimate the minimum distance of codes from algebraic surfaces. This lower bound is generic, i.e. can be applied to any surface, and turns out to be ``liftable'' under finite morphisms, paving the way toward the construction of good codes from towers of surfaces. In the same direction, we establish a criterion for a surface with a fixed finite set of closed points $\mathcal P$ to have an infinite tower of $\ell$--étale covers in which $\mathcal P$ splits totally. We conclude by stating several open problems. In particular, we relate the existence of asymptotically good codes from general type surfaces with a very ample canonical class to the behaviour of their number of rational points with respect to their $K^2$ and coherent Euler characteristic.
