March 3, 2026Open Access

Hierarchical Locally Recoverable Codes on surfaces

Key Points

Hierarchical locally recoverable codes are constructed from surfaces with specific fibrations.
The method yields parameters for codes and includes an explicit count of rational points in certain cases.
Assessment involves projections onto coordinates to derive codes from geometric and arithmetic properties.
This approach highlights the intersection of coding theory and algebraic geometry, expanding research opportunities.

Abstract

We construct locally recoverable codes with hierarchy from surfaces in A³ admitting a fibration by curves of Artin-Schreier or Kummer type. We derive the parameters of our codes by leveraging the geometry and arithmetic of the fibration, which is obtained by projection onto one of the coordinates. As a byproduct, we obtain estimates for (and in one case an explicit count of) the number of rational points in certain families of surfaces.

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Authors

Carolina Araújo

Luana Costa

Beth Malmskog

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Hierarchical Locally Recoverable Codes on surfaces

Key Points

Abstract

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Discussion

Authors

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References and Citations

Citation Network

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Discussion

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