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Distributed storage systems are composed by many unreliable storage nodes over a network. A data file is redundantly stored in multiple storage nodes to provide high reliability. Recently erasure codes with Maximum Distance Separable (MDS) property are gradually employed in distributed storage systems to reduce the cost of reliably storing large amounts of data. Regenerating codes are a class of erasure...
In this paper, we present a new basis of polynomial over finite fields of characteristic two and then apply it to the encoding/decoding of Reed-Solomon erasure codes. The proposed polynomial basis allows that h-point polynomial evaluation can be computed in O(hlog2(h)) finite field operations with small leading constant. As compared with the canonical polynomial basis, the proposed basis improves...
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