Error Decoding of Locally Repairable and Partial MDS Codes

In this work it is shown that locally repairable codes (LRCs) can be list-decoded efficiently beyond the Johnson radius for a large range of parameters by utilizing local error-correction capabilities. The corresponding decoding derived and asymptotic behavior analyzed. A general list-decoding algorithm LRCs achieves proposed along with an explicit realization are subcodes Reed-Solomon (such as, e.g., Tamo-Barg LRCs). Further, probabilistic low complexity unique given its success probability second part considers error partial maximum distance separable (PMDS) through interleaved decoding. For specific class investigated. PMDS codes, there wide which increase their minimum such successful approaches 1 when code length goes to infinity.