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 Fq of size q = O(n). We will refer to the constructed codes as Small- d MSR codes. The sub-packetization level a is given by a = s. ns., 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.