MDS and NMDS Codes from the Extended Twisted Generalized Reed-Solomon Codes
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866911707989803008 |
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| author | Wang, Yanli Chen, Yanxin Yan, Tongjiang |
| author_facet | Wang, Yanli Chen, Yanxin Yan, Tongjiang |
| contents | This paper contributes to maximum distance separable (MDS) and near MDS (NMDS) properties of the extended generalized twisted Reed-Solomon (TGRS) codes. Firstly, a family of extended TGRS (ETGRS) are constructed by appending three columns to the generator matrix of original TGRS codes. Secondly, the necessary and sufficient conditions for these codes to be MDS or almost MDS (AMDS) codes are derived. Then, by analyzing the AMDS properties of their dual codes, the necessary and sufffcient conditions for them to be NMDS codes are established. Furthermore, some examples are given to verify the main results. Finally, we determine the non-generalized Reed-Solomon (non-GRS) characteristics of them via the Schur product method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_23329 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | MDS and NMDS Codes from the Extended Twisted Generalized Reed-Solomon Codes Wang, Yanli Chen, Yanxin Yan, Tongjiang Information Theory This paper contributes to maximum distance separable (MDS) and near MDS (NMDS) properties of the extended generalized twisted Reed-Solomon (TGRS) codes. Firstly, a family of extended TGRS (ETGRS) are constructed by appending three columns to the generator matrix of original TGRS codes. Secondly, the necessary and sufficient conditions for these codes to be MDS or almost MDS (AMDS) codes are derived. Then, by analyzing the AMDS properties of their dual codes, the necessary and sufffcient conditions for them to be NMDS codes are established. Furthermore, some examples are given to verify the main results. Finally, we determine the non-generalized Reed-Solomon (non-GRS) characteristics of them via the Schur product method. |
| title | MDS and NMDS Codes from the Extended Twisted Generalized Reed-Solomon Codes |
| topic | Information Theory |
| url | https://arxiv.org/abs/2605.23329 |