Multilinear Algebra for Distributed Storage

06/16/2020 ∙ by Iwan Duursma, et al. ∙ 0

An (n, k, d, α, β, M)-ERRC (exact-repair regenerating code) is a collection of n nodes used to store a file. For a file of total size M, each node stores α symbols, any k nodes recover the file, and any d nodes repair any other node via sending out β symbols. We establish a multilinear algebra foundation to assemble (n, k, d, α, β, M)-ERRCs for all meaningful (n, k, d) tuples. Our ERRCs tie the α/M-versus-β/M trade-off with cascade codes, the best known construction for this trade-off. We give directions on how these ERRCs repair multiple failures.

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