Non-GRS type MDS and AMDS codes from extended TGRS codes
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866913010169151488 |
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| author | Zhang, Meiying Yang, Shudi Zheng, Yanbin |
| author_facet | Zhang, Meiying Yang, Shudi Zheng, Yanbin |
| contents | Maximum distance separable (MDS) and almost maximum distance separable (AMDS) codes have been widely used in various fields such as communication systems, data storage, and quantum codes because of their algebraic properties and excellent error-correcting capabilities. In this paper, we construct a class of extended twisted generalized Reed-Solomon (TGRS) codes and determine the necessary and sufficient conditions for these codes to be MDS or AMDS. Additionally, we prove that these codes are not equivalent to generalized Reed-Solomon (GRS) codes. As an application, under certain circumstances, we compute the covering radii and deep holes of these codes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_05682 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Non-GRS type MDS and AMDS codes from extended TGRS codes Zhang, Meiying Yang, Shudi Zheng, Yanbin Information Theory Maximum distance separable (MDS) and almost maximum distance separable (AMDS) codes have been widely used in various fields such as communication systems, data storage, and quantum codes because of their algebraic properties and excellent error-correcting capabilities. In this paper, we construct a class of extended twisted generalized Reed-Solomon (TGRS) codes and determine the necessary and sufficient conditions for these codes to be MDS or AMDS. Additionally, we prove that these codes are not equivalent to generalized Reed-Solomon (GRS) codes. As an application, under certain circumstances, we compute the covering radii and deep holes of these codes. |
| title | Non-GRS type MDS and AMDS codes from extended TGRS codes |
| topic | Information Theory |
| url | https://arxiv.org/abs/2604.05682 |