### Current browse context:

math.AG

### Change to browse by:

### References & Citations

# Mathematics > Algebraic Geometry

# Title: Toward good families of codes from towers of surfaces

(Submitted on 6 Feb 2020 (v1), last revised 8 Jun 2020 (this version, v2))

Abstract: 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 $\ell$--\'etale 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.

## Submission history

From: Couvreur Alain [view email]**[v1]**Thu, 6 Feb 2020 12:18:37 GMT (316kb,D)

**[v2]**Mon, 8 Jun 2020 10:10:09 GMT (77kb,D)

Link back to: arXiv, form interface, contact.