Explicit MSR Codes with Optimal Access, Optimal Sub-Packetization and Small Field Size for $d=k+1, k+2, k+3$
Myna Vajha, Balaji Srinivasan Babu, P. Vijay Kumar · 2018
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 \mathbbFQ 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 [1]. To our understanding the codes presented in this paper are the first explicit constructions of MSR codes with having optimal sub-packetization, optimal access and small field size.