Two classes of (r, t)-locally repairable codes

Anyu Wang, Zhifang Zhang, Dongdai Lin
2016 2016 IEEE International Symposium on Information Theory (ISIT)  
Recently, the (r, t)-locally repairable code has attracted a lot of attention due to its potential application in distributed storage systems for hot data. A locally repairable code with locality r and availability t, which is termed an (r, t)-LRC, is a code satisfying the property that the value at each coordinate can be recovered from t disjoint repair sets, each set consists of at most r other coordinates. In this paper, we investigate two constructions of (r, t)-LRCs. The first one is a
more » ... ic code of which the parity check polynomial is closely related to the trace function over finite fields. This code can achieve high availability and large minimum distance. The second one is based on the incidence matrix of linear subspaces in F m q . For some specific parameters, we prove that its information rate is always higher than r r+t which is conjectured to be near to the optimal information rate for (r, t)-LRCs (A. Wang and Z. Zhang, ISIT 2015). By shortening this code in a specially designed way, we obtain (r, t)-LRCs with slightly lower information rate but much more desirable locality r.
doi:10.1109/isit.2016.7541338 dblp:conf/isit/WangZL16 fatcat:l6frfe3qofevhbbrgz6b3s5fey