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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.03034 |
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| _version_ | 1866910199736958976 |
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| author | Liu, Xiaofeng Zhang, Jun Fu, Fang-Wei |
| author_facet | Liu, Xiaofeng Zhang, Jun Fu, Fang-Wei |
| contents | Motivated by the studies of twisted generalized Reed-Solomon (TGRS) codes, we initiate the study of twisted elliptic curve codes (TECCs) in this paper. In particular, we study a class of TECCs with one twist. The parity-check matrices of the TECCs are explicitly given by computing the Weil differentials. Then the sufficient and necessary conditions of self-duality are presented. The minimum distances of the TECCs are also determined. Moreover, examples of MDS, AMDS, self-dual and MDS self-dual TECCs are given. Finally, we calculate the dimensions of the Schur squares of TECCs and show the non-equivalence between TECCs and ECCs/GRS codes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_03034 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a class of twisted elliptic curve codes Liu, Xiaofeng Zhang, Jun Fu, Fang-Wei Information Theory Motivated by the studies of twisted generalized Reed-Solomon (TGRS) codes, we initiate the study of twisted elliptic curve codes (TECCs) in this paper. In particular, we study a class of TECCs with one twist. The parity-check matrices of the TECCs are explicitly given by computing the Weil differentials. Then the sufficient and necessary conditions of self-duality are presented. The minimum distances of the TECCs are also determined. Moreover, examples of MDS, AMDS, self-dual and MDS self-dual TECCs are given. Finally, we calculate the dimensions of the Schur squares of TECCs and show the non-equivalence between TECCs and ECCs/GRS codes. |
| title | On a class of twisted elliptic curve codes |
| topic | Information Theory |
| url | https://arxiv.org/abs/2509.03034 |