A Note on Bandwidth-Optimal Repair Scheme for Reed-Solomon Codes With Low Repair Locality

Reed-Solomon codes can be regarded as polynomials over a finite field
$GF(q^{t})$
evaluated at a set of points, where
$t$
is referred to as the sub-packetization size. In this letter, for the small sub-packetization size regime, we show a bandwidth-optimal linear repair scheme of single failed symbol for Reed-Solomon codes with repair locality smaller than
$n-1$
for the first time, where repair locality refers to the number of the surviving symbols involved in the repair and
$n$
means the code length.