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.

翻译：本文旨在给出从 Deligne-Lusztig 曲面上的射影丛构造的代数几何纠错码参数的下界。基于交截理论的深入运用，我们得以推广先前从高维簇及曲线构造的纠错码。针对标准 Deligne-Lusztig 曲面上秩为 $2$ 的射影丛情形，我们得到了通用界，并给出了来自 $A_{2}$ 型和 ${}^{2}A_{4}$ 型曲面的显式示例。