Back to Search
Start Over
Codes with Hierarchical Locality on Artin-Schreier Surfaces
- Publication Year :
- 2024
-
Abstract
- In this article, we construct codes with hierarchical locality using natural geometric structures in Artin-Schreier surfaces of the form $y^p-y=f(x,z)$. Our main theorem describes the codes, their hierarchical structure and recovery algorithms, and gives parameters. We also develop a family of examples using codes defined over $\mathbb{F}_{p^2}$ on the surface $y^p-y=x^{p+1}z^2+x^2z^{p+1}$. We count the $\mathbb{F}_{p^2}$-rational points on the surface, a topic of more general number theoretic interest, and provide more explicit parameters a better bound on minimum distance for these codes. An additional example and some generalizations are also considered.
- Subjects :
- Mathematics - Number Theory
14G50, 94B27, 11T71
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2405.19533
- Document Type :
- Working Paper