Explicit MSR Codes with Optimal Access, Optimal Sub-Packetization and Small Field Size for $d = k+1, k+2, k+3$
نویسندگان
چکیده
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 FQ having sub-packetization α = qd n q e, 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 [1]. 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.
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An explicit, coupled-layer construction of a high-rate MSR code with low sub-packetization level, small field size and d < (n - 1)
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