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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/2501.09710 |
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| _version_ | 1866929678642577408 |
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| author | Mahak Bhaintwal, Maheshanand |
| author_facet | Mahak Bhaintwal, Maheshanand |
| contents | A code is said to be equidistant if the distance between any two distinct codewords of the code is the same. In this paper, we have studied equidistant single-orbit cyclic and quasi-cyclic subspace codes. The orbit code generated by a subspace $U$ in $\mathbb{F}_{q^n}$ such that the dimension of $U$ over $\mathbb{F}_q$ is $t$ or $n-t$, $\mbox{where}~t=\dim_{\mathbb{F}_q}(\mbox{Stab}(U)\cup\{0\})$, is equidistant and is termed a trivial equidistant orbit code. Using the concept of cyclic difference sets, we have proved that only the trivial equidistant single-orbit cyclic subspace codes exist. Further, we have explored equidistant single-orbit quasi-cyclic subspace codes, focusing specifically on those which are sunflowers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_09710 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On equidistant single-orbit cyclic and quasi-cyclic subspace codes Mahak Bhaintwal, Maheshanand Information Theory A code is said to be equidistant if the distance between any two distinct codewords of the code is the same. In this paper, we have studied equidistant single-orbit cyclic and quasi-cyclic subspace codes. The orbit code generated by a subspace $U$ in $\mathbb{F}_{q^n}$ such that the dimension of $U$ over $\mathbb{F}_q$ is $t$ or $n-t$, $\mbox{where}~t=\dim_{\mathbb{F}_q}(\mbox{Stab}(U)\cup\{0\})$, is equidistant and is termed a trivial equidistant orbit code. Using the concept of cyclic difference sets, we have proved that only the trivial equidistant single-orbit cyclic subspace codes exist. Further, we have explored equidistant single-orbit quasi-cyclic subspace codes, focusing specifically on those which are sunflowers. |
| title | On equidistant single-orbit cyclic and quasi-cyclic subspace codes |
| topic | Information Theory |
| url | https://arxiv.org/abs/2501.09710 |