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arXiv · 2401.11433

Error-Correcting Codes on Projective Bundles over Deligne-Lusztig varieties

Daniel Camazón Portela·Juan Antonio López Ramos
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Abstract

The aim of this article is to give lower bounds on the parameters of algebraic geometric error-correcting codes constructed from projective bundles over Deligne--Lusztig surfaces. The methods based on an intensive use of the intersection theory allow us to extend the codes previously constructed from higher-dimensional varieties, as well as those coming from curves. General bounds are obtained for the case of projective bundles of rank $2$ over standard Deligne-Lusztig surfaces, and some explicit examples coming from surfaces of type $A_{2}$ and ${}^{2}A_{4}$ are given.

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Daniel Camazón Portela, Juan Antonio López Ramos. 2024-01-21. Error-Correcting Codes on Projective Bundles over Deligne-Lusztig varieties. https://doi.org/10.3390/math11143079

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