A family of optimal locally recoverable codes

Itzhak Tamo, Alexander Barg
2014 2014 IEEE International Symposium on Information Theory  
A code over a finite alphabet is called locally recoverable (LRC) 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 codewords are obtained as evaluations of specially constructed polynomials over a finite field, and reduce to a Reed-Solomon code if the locality parameter r is set to be equal to the code
more » ... . The size of the code alphabet for most parameters is only slightly greater than the code length. 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 ("hot data").
doi:10.1109/isit.2014.6874920 dblp:conf/isit/TamoB14 fatcat:phfqvgepo5f7vhzpeausqrd4zu