Localized Error Correction in Projective Space

In this paper, we extend the localized error correction code introduced by L. A. Bassalygo and coworkers from Hamming space to projective space. For constant dimensional localized error correction codes in projective space, we have a lower bound and an upper bound of the capacity, which are asymptotically tight when
z
<;
x
≤ [(
n
-
z
)/2], where
x
,
z
, and
n
are dimensions of codewords, error configurations, and the ground space, respectively. We determine the capacity of nonconstant dimensional localized error correction codes when
z
<; [(
n
)/3].