Anticanonical codes from del Pezzo surfaces with Picard rank one
Algebraic Geometry
2019-03-25 v1 Information Theory
math.IT
Abstract
We construct algebraic geometric codes from del Pezzo surfaces and focus on the ones having Picard rank one and the codes associated to the anticanonical class. We give explicit constructions of del Pezzo surfaces of degree 4, 5 and 6, compute the parameters of the associated anticanonical codes and study their isomorphisms arising from the automorphisms of the surface. We obtain codes with excellent parameters and some of them turn out to beat the best known codes listed on the database codetable.
Cite
@article{arxiv.1903.09397,
title = {Anticanonical codes from del Pezzo surfaces with Picard rank one},
author = {Régis Blache and Alain Couvreur and Emmanuel Hallouin and David Madore and Jade Nardi and Matthieu Rambaud and Hugues Randriam},
journal= {arXiv preprint arXiv:1903.09397},
year = {2019}
}