Girth-Based Sequential-Recovery LRCs

Abstract

In this paper, we prove that a linear block code with girth $2(t+1)$ is a $t$ -sequential-recovery locally repairable codes (LRCs) with locality $r$ if its parity-check matrix has column weight at least 2 and row weight at most $r+1$ . This gives a new connection between sequential-recovery LRCs and linear block codes. We also derive that the repair time of the $t$ -sequential-recovery LRCs from the linear block codes by this connection is at most $\lceil t/2 \rceil $ .

Keywords

• Locally repairable codes
• joint sequential-parallel-recovery
• girth
• repair time