Error-Correcting Codes on Projective Bundles over Deligne–Lusztig Varieties

Daniel Camazón Portela () and Juan Antonio López Ramos
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Daniel Camazón Portela: Department of Mathematics, University of Almería, 04120 Almería, Spain
Juan Antonio López Ramos: Department of Mathematics, University of Almería, 04120 Almería, Spain

Mathematics, 2023, vol. 11, issue 14, 1-12

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.

Keywords: error-correcting codes; Deligne–Lusztig varieties; projective bundles; intersection theory (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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