New MDS codes of non-GRS type and NMDS codes
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866929628494430208 |
|---|---|
| author | Zhi, Yujie Zhu, Shixin |
| author_facet | Zhi, Yujie Zhu, Shixin |
| contents | Maximum distance separable (MDS) and near maximum distance separable (NMDS) codes have been widely used in various fields such as communication systems, data storage, and quantum codes due to their algebraic properties and excellent error-correcting capabilities. This paper focuses on a specific class of linear codes and establishes necessary and sufficient conditions for them to be MDS or NMDS. Additionally, we employ the well-known Schur method to demonstrate that they are non-equivalent to generalized Reed-Solomon codes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_03693 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | New MDS codes of non-GRS type and NMDS codes Zhi, Yujie Zhu, Shixin Information Theory Maximum distance separable (MDS) and near maximum distance separable (NMDS) codes have been widely used in various fields such as communication systems, data storage, and quantum codes due to their algebraic properties and excellent error-correcting capabilities. This paper focuses on a specific class of linear codes and establishes necessary and sufficient conditions for them to be MDS or NMDS. Additionally, we employ the well-known Schur method to demonstrate that they are non-equivalent to generalized Reed-Solomon codes. |
| title | New MDS codes of non-GRS type and NMDS codes |
| topic | Information Theory |
| url | https://arxiv.org/abs/2406.03693 |