A Construction of Optimal $(r,\delta)$ -Locally Recoverable Codes

Locally recoverable codes (LRCs) play a significant role in distributed and cloud storage systems. The key ingredient for constructing such optimal LRCs is to characterize the parity-check matrix for LRCs. In this letter based on the parity-check matrix for generalized Reed-Solomon codes we mainly present new constructions of optimal
$(r,\delta )$
-locally recoverable codes with unbounded lengths in terms of the properties of the Vandermonde matrices, of which the parameters contain the known ones.