Explicit MSR Codes with Optimal Access, Optimal Sub-Packetization and Small Field Size for d = k+1, k+2, k+3

04/02/2018

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by   Myna Vajha, et al.

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This paper presents the construction of an explicit, optimal-access, high-rate MSR code for any (n,k,d=k+1,k+2,k+3) parameters over the finite field having sub-packetization α = q^n/q, where q=d-k+1 and Q = O(n). The sub-packetization of the current construction meets the lower bound proven in a recent work by Balaji et al. in BalKum. To our understanding the codes presented in this paper are the first explicit constructions of MSR codes with d<(n-1) having optimal sub-packetization, optimal access and small field size.