  For a systematic erasure code, update complexity (UC) is defined as the
maximum number of parity blocks needed to be changed when some information
blocks are updated. Locally repairable codes (LRCs) have been recently proposed
and used in real-world distributed storage systems. In this paper, update
complexity for optimal LRC is studied and both lower and upper bounds on UC are
established in terms of length (n), dimension (k), minimum distance (d), and
locality (r) of the code, when (r+1)|n. Furthermore, a class of optimal LRCs
with small UC is proposed. Our proposed LRCs could be of interest as they
improve UC without sacrificing optimality of the code.
