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 number d of helper nodes. The construction is valid for any parameter set ( n, k, d ) with d ∈ { k +1, k +2, k +3} and employs a finite field F q of size q = O(n) . We will refer to the constructed codes as Small-d MSR codes. The sub-packetization level α is given by α = 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.