Locally recoverable codes are error-correcting codes with the additional
property that every symbol of any codeword can be recovered from a small
set of other symbols. This property is particularly desirable in cloud
storage applications. A locally recoverable code is said to have availability
if each
position has
disjoint recovery sets. Hermitian-lifted codes are locally recoverable codes with high
availability first described by López, Malmskog, Matthews, Piñero-Gonzáles,
and Wootters. The codes are based on the well-known Hermitian curve and
incorporate the novel technique of lifting to increase the rate of the code. López et
al. (2021) provided a lower bound for the rate of the codes defined over fields with
characteristic 2. This paper generalizes their work to show that the rate of
Hermitian-lifted codes is bounded below by a positive constant depending on
, when
for any
odd prime
.
