A New Construction of Optimal (<i>r</i>, δ) Locally Recoverable Codes
Guanghui Zhang
Abstract
Locally recoverable codes (LRCs) have a great significance in distributed storage systems, and have received considerable attention in recent years. In particular, it is a challenging task to construct optimal (r, δ)-LRCs, meaning (r, δ)-LRCs whose minimum distances attain Singleton-type bound. In this letter, we investigate the construction of a family of optimal (r, δ)-LRCs via generalized Reed-Solomon codes (GRS codes). Our strategy is to equip parity-check matrices for optimal (r, δ)-LRCs with the Vandermonde structure. Furthermore, based on these new optimal (r, δ)-LRCs we present a family of optimal locally recoverable codes with hierarchical locality (H-LRCs). The parameters of our results are not covered in the literature.