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

Author

Listed:
  • Daniel Camazón Portela

    (Department of Algebra, Analysis, Geometry and Topology, University of Valladolid, 47011 Valladolid, Spain
    These authors contributed equally to this work.)

  • Juan Antonio López Ramos

    (Department of Mathematics, University of Almería, 04120 Almería, Spain
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Daniel Camazón Portela & Juan Antonio López Ramos, 2023. "Error-Correcting Codes on Projective Bundles over Deligne–Lusztig Varieties," Mathematics, MDPI, vol. 11(14), pages 1-12, July.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:14:p:3079-:d:1192551
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