Codes with Hierarchical Locality on Artin-Schreier Surfaces
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908133802115072 |
|---|---|
| author | Berg, Jennifer Malmskog, Beth West, Mckenzie |
| author_facet | Berg, Jennifer Malmskog, Beth West, Mckenzie |
| contents | 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 use elementary methods to count the $\mathbb{F}_{p^2}$-rational points on the surface, enabling us to provide explicit hierarchical parameters and a better bound on minimum distance for these codes. An additional example and some generalizations are also considered. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_19533 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Codes with Hierarchical Locality on Artin-Schreier Surfaces Berg, Jennifer Malmskog, Beth West, Mckenzie Number Theory 14G50, 94B27, 11T71 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 use elementary methods to count the $\mathbb{F}_{p^2}$-rational points on the surface, enabling us to provide explicit hierarchical parameters and a better bound on minimum distance for these codes. An additional example and some generalizations are also considered. |
| title | Codes with Hierarchical Locality on Artin-Schreier Surfaces |
| topic | Number Theory 14G50, 94B27, 11T71 |
| url | https://arxiv.org/abs/2405.19533 |