Efficient node repair is a central requirement in distributed storage systems, particularly in high-rate erasure-coded deployments where repair traffic directly affects network overhead and recovery cost. Piggybacking codes reduce the repair bandwidth of MDS array codes while keeping the sub-packetization level small. However, existing piggybacking constructions often rely on restrictive piggyback-function designs to preserve the MDS property over small fields, which limits their repair-bandwidth reduction. We propose {\em conjugate-piggybacking} codes, a new class of MDS array codes that jointly design piggyback functions and conjugate transformations under small sub-packetization. The proposed construction improves repair efficiency while preserving the MDS property over moderate field sizes. In particular, it enables some parity nodes to achieve optimal repair bandwidth and reduces the overall repair bandwidth compared with existing piggybacking-based designs. We analyze the MDS property and repair bandwidth of the proposed codes and evaluate them against existing piggybacking codes under high-code-rate settings over $\mathbb{F}_{2^8}$. We further conduct a repair-traffic simulation under uniform single-node failures to quantify the expected traffic reduction in storage-oriented settings. The results show that our construction consistently achieves lower repair bandwidth than related piggybacking codes and reduces expected repair traffic compared with conventional RS repair. These gains are obtained at the cost of a slightly larger field size, revealing a practical trade-off between repair efficiency and field-size overhead for high-rate distributed storage.

翻译：高效的节点修复是分布式存储系统的核心需求，尤其是在高码率纠删码部署场景中，修复流量直接影响网络开销与恢复成本。Piggybacking 码可在保持小子包化水平的同时降低 MDS 阵列码的修复带宽。然而，现有 Piggybacking 构造常依赖限制性的 Piggyback 函数设计来在小域上保持 MDS 性质，这限制了其修复带宽的降低效果。本文提出{\em 共轭-Piggybacking}码——一种在小子包化条件下联合设计 Piggyback 函数与共轭变换的新型 MDS 阵列码。所提构造在中等域大小上保持 MDS 性质的同时提升了修复效率。特别地，它使部分校验节点可实现最优修复带宽，并与现有基于 Piggybacking 的设计相比降低了整体修复带宽。我们分析了所提码的 MDS 性质与修复带宽，并在 $\mathbb{F}_{2^8}$ 上的高码率设置下将其与现有 Piggybacking 码进行对比评估。进一步地，我们开展了均匀单节点故障下的修复流量仿真，以量化存储场景中预期流量的降低效果。结果表明，我们的构造始终比相关 Piggybacking 码实现更低的修复带宽，且相比传统 RS 修复降低了预期修复流量。这些增益以略大的域大小为代价，揭示了高码率分布式存储中修复效率与域大小开销之间的实际权衡。