A family of optimal locally recoverable codes

A code over a finite alphabet is called locally recoverable code (LRC code) if every symbol in the encoding is a function of a small number (at most r) other symbols. We present a family of LRC codes that attain the maximum possible value of the distance for a given locality parameter and code cardinality. The codes can be constructed over a finite field alphabet of any size that exceeds the code length. The codewords are obtained as evaluations of specially constructed polynomials over a finite field, and reduce to Reed-Solomon codes if the locality parameter r is set to be equal to the code dimension. The recovery procedure is performed by polynomial interpolation over r points. We also construct codes with several disjoint recovering sets for every symbol. This construction enables the system to conduct several independent and simultaneous recovery processes of a specific symbol by accessing different parts of the codeword. This property enables high availability of frequently accessed data.