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

Abstract

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 $\beta$ pieces of data per node. For minimum storage regenerating (MSR) codes, ${d \geq 2 k - 3}$ has been proved. However, as far as we know, there is no construction of exact-repair MSR codes with ${d= 2 k - 3}$ and ${\beta = 1}$ at present. In this letter, we give the first construction of [6, 4, 5] MSR codes with ${\beta = 1}$ , 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 ${F_{4}}$ .