A New Construction of Exact-Repair MSR Codes Using Linearly Dependent Vectors

Regenerating codes focus on the efficient repair of node failures. In an [n, k, d] regenerating code system, any k nodes can retrieve the original data and any d nodes can repair a failed node by giving out β pieces of data per node. For minimum storage regenerating (MSR) codes, d ≥ 2k - 3 has been proved. However, as far as we know, there is no construction of exact-repair MSR codes with d = 2k - 3 and β = 1 at present. In this letter, we give the first construction of [6, 4, 5] MSR codes with β = 1, which can perform exact repair of all nodes. Employing the technique of linearly dependent vectors, our codes can be constructed over a small finite field F
₄
.