How to Expand a Self-orthogonal Code
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909916574253056 |
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| author | Kim, Jon-Lark Liu, Hongwei Luo, Jinquan |
| author_facet | Kim, Jon-Lark Liu, Hongwei Luo, Jinquan |
| contents | In this paper, we show how to expand Euclidean/Hermitian self-orthogonal code preserving their orthogonal property. Our results show that every $k$-dimension Hermitian self-orthogonal code is contained in a $(k+1)$-dimensional Hermitian self-orthogonal code. Also, for $k< n/2-1$, every $[n,k]$ Euclidean self-orthogonal code is contained in an $[n,k+1]$ Euclidean self-orthogonal code. Moreover, for $k=n/2-1$ and $p=2$, we can also fulfill the expanding process. But for $k=n/2-1$ and $p$ odd prime, the expanding process can be fulfilled if and only if an extra condition must be satisfied. We also propose two feasible algorithms on these expanding procedures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_17503 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | How to Expand a Self-orthogonal Code Kim, Jon-Lark Liu, Hongwei Luo, Jinquan Information Theory Combinatorics 94B05 In this paper, we show how to expand Euclidean/Hermitian self-orthogonal code preserving their orthogonal property. Our results show that every $k$-dimension Hermitian self-orthogonal code is contained in a $(k+1)$-dimensional Hermitian self-orthogonal code. Also, for $k< n/2-1$, every $[n,k]$ Euclidean self-orthogonal code is contained in an $[n,k+1]$ Euclidean self-orthogonal code. Moreover, for $k=n/2-1$ and $p=2$, we can also fulfill the expanding process. But for $k=n/2-1$ and $p$ odd prime, the expanding process can be fulfilled if and only if an extra condition must be satisfied. We also propose two feasible algorithms on these expanding procedures. |
| title | How to Expand a Self-orthogonal Code |
| topic | Information Theory Combinatorics 94B05 |
| url | https://arxiv.org/abs/2511.17503 |