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arXiv · 2605.10508

Optimal Repair Bandwidth and Repair I/O of $(n,n-2,2)$ MDS Array Codes

Huawei Wu
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Abstract

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.

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Huawei Wu. 2026-05-11. Optimal Repair Bandwidth and Repair I/O of $(n,n-2,2)$ MDS Array Codes. https://arxiv.org/abs/2605.10508

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