Two Families of Linear Codes Containing Non-GRS MDS Codes
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915917047267328 |
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| author | Abdukhalikov, Kanat Verma, Gyanendra K. |
| author_facet | Abdukhalikov, Kanat Verma, Gyanendra K. |
| contents | We construct two new families of linear codes by modifying the generator matrices of generalized Reed-Solomon (GRS) codes. For these codes, we explicitly derive parity-check matrices and establish necessary and sufficient conditions ensuring the MDS property. Additionally, we explore subfamilies within these constructions that are non-GRS MDS codes. We also characterize their self-orthogonal and self-dual properties and present some explicit constructions and examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_13429 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Two Families of Linear Codes Containing Non-GRS MDS Codes Abdukhalikov, Kanat Verma, Gyanendra K. Information Theory 94B05, 94B65 We construct two new families of linear codes by modifying the generator matrices of generalized Reed-Solomon (GRS) codes. For these codes, we explicitly derive parity-check matrices and establish necessary and sufficient conditions ensuring the MDS property. Additionally, we explore subfamilies within these constructions that are non-GRS MDS codes. We also characterize their self-orthogonal and self-dual properties and present some explicit constructions and examples. |
| title | Two Families of Linear Codes Containing Non-GRS MDS Codes |
| topic | Information Theory 94B05, 94B65 |
| url | https://arxiv.org/abs/2512.13429 |