Recently Reed-Solomon (RS) codes were shown to possess a repair scheme that supports repair of failed nodes with optimal repair bandwidth. In this paper, we extend this result in two directions. First, we propose a new repair scheme for the RS codes constructed in [Tamo-Ye-Barg, {\em IEEE Transactions on Information Theory}, vol. 65, May 2019] and show that our new scheme is robust to erroneous information provided by the helper nodes while maintaining the optimal repair bandwidth. Second, we construct a new family of RS codes with optimal access for the repair of any single failed node. We also show that the constructed codes can accommodate both features, supporting optimal-access repair with optimal error-correction capability. Going beyond RS codes, we also prove that any scalar MDS code with optimal repair bandwidth allows for a repair scheme with optimal access property.

中文翻译：

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为修复 Reed-Solomon 代码启用最佳访问和纠错

最近，Reed-Solomon (RS) 代码被证明拥有一种修复方案，支持以最佳修复带宽修复故障节点。在本文中，我们将这个结果扩展到两个方向。首先，我们为 [Tamo-Ye-Barg, {\em IEEE Transactions on Information Theory}, vol. 中构建的 RS 代码提出了一种新的修复方案。65, May 2019] 并表明我们的新方案对辅助节点提供的错误信息具有鲁棒性，同时保持最佳修复带宽。其次，我们构建了一个新的 RS 代码系列，具有用于修复任何单个故障节点的最佳访问权限。我们还表明，构建的代码可以适应这两种特征，支持具有最佳纠错能力的最佳访问修复。超越RS码，