Small-d MSR Codes With Optimal Access, Optimal Sub-Packetization, and Linear Field Size
Myna Vajha, S. B. Balaji, P. Vijay Kumar · IEEE Transactions on Information Theory · 2023
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$d \in \{k+1, k+2, k+3\}$and employs a finite field$\mathbb {F}_{q}$of size$q=O(n)$. We will refer to the constructed codes as$\text {Small-}\mathsf {d}$MSR codes. The sub-packetization level$\alpha $is given by$\alpha = s^{{\lceil \frac {n}{s}\rceil }}$, where$s=d-k+1$. By an earlier result on the sub-packetization level for optimal-access MSR codes, this is the smallest value possible.