Girth-Based Sequential-Recovery LRCs

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 $
.