Improved Constructions for Optimal Multi-erasure Locally Recoverable Codes for Big Data Storage

Multi-erasure locally recoverable codes play a very significant role in distributed data storage. The advantage of multi-erasure locally recoverable codes is that it has local and global erasure-correcting characteristics. Recently, based on classical algebraic geometry codes, Huang et al. constructed a family of explicit optimal multi-erasure locally recoverable codes over small finite fields F4. In this work, based on the work of Huang et al., we use cyclic codes to construct a family of new optimal multi-erasure locally recoverable codes over small finite fields F3. It turns out that our multi-erasure locally recoverable codes have smaller finite fields than the previously known results.