Construction Of Optimal (r,δ) Locally Repairable Codes

The use of large-scale cloud storage and distributed systems is so widespread that disk failures become the norm rather than the exception.Copying data across disks is the most straightforward way to protect data from various failures.Given the high storage overhead of doing so,an alternative solution is to use the MDS code as the storage code,which encodes k information bits and n-k check bits into characters of length n and stores them on n disks.Such a storage method of course greatly optimizes the redundancy,but for a general MDS code,when a node fails,we need to visit the remaining k intact nodes to recover it.In order to effectively improve the repair efficiency,Huang and other investigators introduced the locality r in their study of data storage systems to reduce the number of nodes that need to be visited in the process of repairing faults,and to ensure that one error node only need to visit the remaining r(?)k intact nodes to be recovered.So far,the locally repairable codes is just a linear block code with a locality parameter r added,and it’s initial definition is only for the case of correcting one error.The purpose of this paper is to promote the above situation.That is,under the premise of discussing good locally repairable codes,using the automorphism groups of rational function fields to construct optimal(r,δ)(δ≥2)locally repairable codes.