Optimal Repair Bandwidth and Repair I/O of $(n,n-2,2)$ MDS Array Codes
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917480612495360 |
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| author | Wu, Huawei |
| author_facet | Wu, Huawei |
| contents | We give a complete determination of the exact optimal worst-case repair bandwidth and repair I/O for linear exact repair of $(n,n-2,2)$ MDS array codes over every finite field $\mathbb{F}_q$ and for every admissible code length $3\le n\le q^2+1$. For repair bandwidth, we prove that the optimum is governed, up to a short explicit list of small exceptional cases, by the maximum of the sharpened $n$-only lower bound $\lceil(5n-8)/4\rceil$ and the projective counting, equivalently incidence-multiplicity, bound $2n-q-3$. For repair I/O, we obtain the analogous exact formula with $\lceil(4n-6)/3\rceil$ in place of $\lceil(5n-8)/4\rceil$, with the single special value at $n=4$. Thus, we completely resolve the first non-trivial redundancy and sub-packetization regime $(r,\ell)=(2,2)$ for both repair bandwidth and repair I/O. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_10508 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Optimal Repair Bandwidth and Repair I/O of $(n,n-2,2)$ MDS Array Codes Wu, Huawei Information Theory Discrete Mathematics Combinatorics We give a complete determination of the exact optimal worst-case repair bandwidth and repair I/O for linear exact repair of $(n,n-2,2)$ MDS array codes over every finite field $\mathbb{F}_q$ and for every admissible code length $3\le n\le q^2+1$. For repair bandwidth, we prove that the optimum is governed, up to a short explicit list of small exceptional cases, by the maximum of the sharpened $n$-only lower bound $\lceil(5n-8)/4\rceil$ and the projective counting, equivalently incidence-multiplicity, bound $2n-q-3$. For repair I/O, we obtain the analogous exact formula with $\lceil(4n-6)/3\rceil$ in place of $\lceil(5n-8)/4\rceil$, with the single special value at $n=4$. Thus, we completely resolve the first non-trivial redundancy and sub-packetization regime $(r,\ell)=(2,2)$ for both repair bandwidth and repair I/O. |
| title | Optimal Repair Bandwidth and Repair I/O of $(n,n-2,2)$ MDS Array Codes |
| topic | Information Theory Discrete Mathematics Combinatorics |
| url | https://arxiv.org/abs/2605.10508 |