
Multilinear Algebra for Distributed Storage
An (n, k, d, α, β, M)ERRC (exactrepair regenerating code) is a collect...
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Explicit Construction of Minimum Storage RackAware Regenerating Codes for All Parameters
We consider the rackaware storage system where n=n̅u nodes are organize...
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Storage Codes with Flexible Number of Nodes
This paper presents flexible storage codes, a class of errorcorrecting ...
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Scalar MSCR Codes via the Product Matrix Construction
An (n,k,d) cooperative regenerating code provides the optimalbandwidth ...
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Achieving Secrecy Capacity of Minimum Storage Regenerating Codes for all Feasible (n, k, d) Parameter Values
This paper addresses the problem of constructing secure exactrepair reg...
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On the Duality and File Size Hierarchy of Fractional Repetition Codes
Distributed storage systems that deploy erasure codes can provide better...
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Correctable Erasure Patterns in Product Topologies
Locality enables storage systems to recover failed nodes from small subs...
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Multilinear Algebra for Minimum Storage Regenerating Codes
An (n, k, d, α)MSR (minimum storage regeneration) code is a set of n nodes used to store a file. For a file of total size kα, each node stores α symbols, any k nodes recover the file, and any d nodes can repair any other node via each sending out α/(dk+1) symbols. In this work, we explore various ways to reexpress the infamous productmatrix construction using skewsymmetric matrices, polynomials, symmetric algebras, and exterior algebras. We then introduce a multilinear algebra foundation to produce (n, k, (k1)t/t1, k1t1)MSR codes for general t≥2. At the t=2 end, they include the productmatrix construction as a special case. At the t=k end, we recover determinant codes of mode m=k; further restriction to n=k+1 makes it identical to the layered code at the MSR point. Our codes' subpacketization level—α—is independent of n and small. It is less than L^2.8(dk+1), where L is Alrabiah–Guruswami's lower bound on α. Furthermore, it is less than other MSR codes' α for a subset of practical parameters. We offer hints on how our code repairs multiple failures at once.
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