Small-d MSR Codes With Optimal Access, Optimal Sub-Packetization, and Linear Field Size

This paper presents an explicit construction of a class of optimal-access, minimum storage regenerating (MSR) codes, for small values of the numberdof helper nodes. The construction is valid for any parameter set$(n,k,d)$withd ∈ +1, k+2, k+3 employs a finite fieldFqof size$q=O(n)$. We will refer to the constructed codes asSmall-dMSR codes. The sub-packetization levelαis given byα = s^ n/s, where$s=d-k+1$. By an earlier result on the sub-packetization level for optimal-access MSR codes, this is the smallest value possible.