Extremal Self-Dual Codes and Linear Complementary Dual Codes from Double Circulant Codes
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909502926749696 |
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| author | Han, Wenyu Yan, Tongjiang Yan, Ming |
| author_facet | Han, Wenyu Yan, Tongjiang Yan, Ming |
| contents | This paper explores extremal self-dual double circulant (DC) codes and linear complementary dual (LCD) codes of arbitrary length over the Galois field $\mathbb F_2$. We establish the sufficient and necessary conditions for DC codes and bordered DC codes to be self-dual and identify the conditions for self-dual DC codes of length up to 44 to be extremal or non-extremal. Additionally, The self-duality and extremality between DC codes and bordered DC codes are also examined. Finally, sufficient conditions for bordered DC codes to be LCD codes over $\mathbb F_2$ under Euclidean inner product are presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_14378 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extremal Self-Dual Codes and Linear Complementary Dual Codes from Double Circulant Codes Han, Wenyu Yan, Tongjiang Yan, Ming Information Theory This paper explores extremal self-dual double circulant (DC) codes and linear complementary dual (LCD) codes of arbitrary length over the Galois field $\mathbb F_2$. We establish the sufficient and necessary conditions for DC codes and bordered DC codes to be self-dual and identify the conditions for self-dual DC codes of length up to 44 to be extremal or non-extremal. Additionally, The self-duality and extremality between DC codes and bordered DC codes are also examined. Finally, sufficient conditions for bordered DC codes to be LCD codes over $\mathbb F_2$ under Euclidean inner product are presented. |
| title | Extremal Self-Dual Codes and Linear Complementary Dual Codes from Double Circulant Codes |
| topic | Information Theory |
| url | https://arxiv.org/abs/2502.14378 |