Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.18175 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916861391667200 |
|---|---|
| author | Zhou, Kun Cao, Meng |
| author_facet | Zhou, Kun Cao, Meng |
| contents | Locally repairable codes (LRCs) play a crucial role in mitigating data loss in large-scale distributed and cloud storage systems. This paper establishes a unified decomposition theorem for general optimal $(r,δ)$-LRCs. Based on this, we obtain that the local protection codes of general optimal $(r,δ)$-LRCs are MDS codes with the same minimum Hamming distance $δ$. We prove that for general optimal $(r,δ)$-LRCs, their minimum Hamming distance $d$ always satisfies $d\geq δ$. We fully characterize the optimal quantum $(r,δ)$-LRCs induced by classical optimal $(r,δ)$-LRCs that admit a minimal decomposition. We construct three infinite families of optimal quantum $(r,δ)$-LRCs with flexible parameters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_18175 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal Quantum $(r,δ)$-Locally Repairable Codes via Classical Ones Zhou, Kun Cao, Meng Quantum Physics Locally repairable codes (LRCs) play a crucial role in mitigating data loss in large-scale distributed and cloud storage systems. This paper establishes a unified decomposition theorem for general optimal $(r,δ)$-LRCs. Based on this, we obtain that the local protection codes of general optimal $(r,δ)$-LRCs are MDS codes with the same minimum Hamming distance $δ$. We prove that for general optimal $(r,δ)$-LRCs, their minimum Hamming distance $d$ always satisfies $d\geq δ$. We fully characterize the optimal quantum $(r,δ)$-LRCs induced by classical optimal $(r,δ)$-LRCs that admit a minimal decomposition. We construct three infinite families of optimal quantum $(r,δ)$-LRCs with flexible parameters. |
| title | Optimal Quantum $(r,δ)$-Locally Repairable Codes via Classical Ones |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2507.18175 |