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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/2507.18175 |
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Table of 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.