Toward good families of codes from towers of surfaces

Alain Couvreur; Philippe Lebacque; Marc Perret

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arXiv · 2002.02220

Toward good families of codes from towers of surfaces

Alain Couvreur·Philippe Lebacque·Marc Perret

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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.

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BibTeX RIS

Alain Couvreur, Philippe Lebacque, Marc Perret. 2020-02-06. Toward good families of codes from towers of surfaces. https://arxiv.org/abs/2002.02220

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