Constructions of optimal locally repairable codes over small fields
LIU MuLan, ZHANG ZhiFang, XU Jing-ke · Scientia Sinica Mathematica · 2017
Locally repairable codes is an attractive research object in recent years. A code coordinate has locality $r$ if the value of this coordinate can be recovered as a function of the values of at most $r$ other coordinates. This is an important property for reducing the repair complexity in distributed storage systems. In this paper, we consider the constructions of optimal locally repairable codes over finite fields with size smaller than the code length $n$. Specifically, over the finite field $\mathbb{F}_q$ with $q=\frac{r}{r+1}n+1$, we construct two classes of optimal locally repairable codes with $r=2, d=6$ and $d=r+1$ respectively.