A Systematic Construction of MDS Codes with Small Sub-packetization Level and Near Optimal Repair Bandwidth
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In the literature, all the known high-rate MDS codes with the optimal repair bandwidth possess a significantly large sub-packetization level, which may prevent the codes to be implemented in practical systems. To build MDS codes with small sub-packetization level, existing constructions and theoretical bounds imply that one may sacrifice the optimality of the repair bandwidth. Partly motivated by the work of Tamo et al. (IEEE Trans. Inform. Theory, 59(3), 1597-1616, 2013), in this paper, we present a powerful transformation that can greatly reduce the sub-packetization level of any MDS codes with respect to the same code length n. As applications of the transformation, four high-rate MDS codes having both small sub-packetization level and near optimal repair bandwidth can be obtained, where two of them are also explicit and the required field sizes are comparable to the code length n. Additionally, we propose another explicit MDS code that have small sub-packetization level, near optimal repair bandwidth, and the optimal update property. The required field size is also comparable to the code length n.
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