A locally recoverable (LRC) code is a code that enables a simple recovery of an erased symbol by accessing only a small number of other symbols. We present several new combinatorial bounds on LRC codes including the locality-aware sphere packing and Plotkin bounds. We also develop an approach to linear programming (LP) bounds on LRC codes. The resulting LP bound gives better estimates in examples than the other upper bounds known in the literature.
['Sihuang Hu', 'Itzhak Tamo', 'Alexander Barg']
Combinatorial and LP bounds for LRC codes