A Generic Construction on Self-orthogonal Algebraic Geometric Codes and Its Applications
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909632070418432 |
|---|---|
| author | Wang, Puyin Luo, Jinquan |
| author_facet | Wang, Puyin Luo, Jinquan |
| contents | In the realm of algebraic geometric (AG) codes, characterizing dual codes has long been a challenging task. In this paper we introduces a generalized criterion to characterize self-orthogonality of AG codes based on residues, drawing upon the rich algebraic structures of finite fields and the geometric properties of algebraic curves. We also present a generic construction of self-orthogonal AG codes from self-dual MDS codes. Using these approaches, we construct several families of self-dual and almost self-dual AG codes. These codes combine two merits: good performance as AG code whose parameters are close to the Singleton bound together with Euclidean (or Hermtian) self-dual/self-orthogonal property. Furthermore, some AG codes with Hermitian self-orthogonality can be applied to construct quantum codes with notably good parameters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_00994 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Generic Construction on Self-orthogonal Algebraic Geometric Codes and Its Applications Wang, Puyin Luo, Jinquan Information Theory 94B27 In the realm of algebraic geometric (AG) codes, characterizing dual codes has long been a challenging task. In this paper we introduces a generalized criterion to characterize self-orthogonality of AG codes based on residues, drawing upon the rich algebraic structures of finite fields and the geometric properties of algebraic curves. We also present a generic construction of self-orthogonal AG codes from self-dual MDS codes. Using these approaches, we construct several families of self-dual and almost self-dual AG codes. These codes combine two merits: good performance as AG code whose parameters are close to the Singleton bound together with Euclidean (or Hermtian) self-dual/self-orthogonal property. Furthermore, some AG codes with Hermitian self-orthogonality can be applied to construct quantum codes with notably good parameters. |
| title | A Generic Construction on Self-orthogonal Algebraic Geometric Codes and Its Applications |
| topic | Information Theory 94B27 |
| url | https://arxiv.org/abs/2506.00994 |