Hermitian Self-dual Generalized Reed-Solomon Codes
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914310529220608 |
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| author | Zhao, Chun'e Ma, Wenping |
| author_facet | Zhao, Chun'e Ma, Wenping |
| contents | Maximum Distance Separable (MDS) self-dual codes are of significant theoretical and practical importance. Generalized Reed-Solomon (GRS) codes are the most prominent MDS codes. Correspondingly there have been many research on constructions of Euclidean self-dual MDS codes by using GRS codes. However, the study on Hermitian self-dual GRS codes is relatively limited. Since Hermitian self-dual GRS codes do not exist for $n>q+1$, this paper is devoted to an investigation of GRS codes in the case where $n\le q+1$. First, we prove that when $n\leq q+1$, there are only two classes of Hermitian self-dual GRS codes, confirming the conjecture in [13] and providing its proof simultaneously. Second, we present two explicit construction methods. Thus, the existence and construction of Hermitian self-dual GRS codes are fully solved. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_06377 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Hermitian Self-dual Generalized Reed-Solomon Codes Zhao, Chun'e Ma, Wenping Information Theory Maximum Distance Separable (MDS) self-dual codes are of significant theoretical and practical importance. Generalized Reed-Solomon (GRS) codes are the most prominent MDS codes. Correspondingly there have been many research on constructions of Euclidean self-dual MDS codes by using GRS codes. However, the study on Hermitian self-dual GRS codes is relatively limited. Since Hermitian self-dual GRS codes do not exist for $n>q+1$, this paper is devoted to an investigation of GRS codes in the case where $n\le q+1$. First, we prove that when $n\leq q+1$, there are only two classes of Hermitian self-dual GRS codes, confirming the conjecture in [13] and providing its proof simultaneously. Second, we present two explicit construction methods. Thus, the existence and construction of Hermitian self-dual GRS codes are fully solved. |
| title | Hermitian Self-dual Generalized Reed-Solomon Codes |
| topic | Information Theory |
| url | https://arxiv.org/abs/2602.06377 |