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Optimal repair schemes for some families of full-length reed-solomon codes

机译：一些全长芦苇-所罗门密码系列的最佳维修方案

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Reed-Solomon codes have found many applications in practical storage systems, but were until recently considered unsuitable for distributed storage applications due to the widely-held belief that they have poor repair bandwidth. The work of Guruswami and Wootters (STOC'16) has shown that one can actually perform bandwidth-efficient linear repair with Reed-Solomon codes: When the codes are over the field Fqt and the number of parities r ≥ q, where (t − s) divides t, there exists a linear scheme that achieves a repair bandwidth of (n − 1)(t − s) logg q bits. We extend this result by showing the existence of such a linear repair scheme for every 1 ≤ s < t. Moreover, our new schemes are optimal among all linear repair schemes for Reed-Solomon codes when n = qt and r = q. Additionally, we improve the lower bound on the repair bandwidth for Reed-Solomon codes, also established in the work of Guruswami and Wootters.
机译：Reed-Solomon代码在实际的存储系统中发现了许多应用，但是直到最近，由于人们普遍认为它们的修复带宽较差，人们认为Reed-Solomon代码不适合于分布式存储应用。 Guruswami和Wootters（STOC'16）的工作表明，人们实际上可以使用Reed-Solomon码执行带宽有效的线性修复：当代码在Fqt字段上并且奇偶数r≥q时，其中（t − s）除以t，则存在一个线性方案，该方案可实现（n-1）（t-s）logg q位的修复带宽。我们通过显示每1≤s

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