Optimal Constacyclic Locally Repairable Codes

摘要

Being part of distributed storage systems, locally repairable codes (LRCs) have drawn great attention in the past years. Inspired by a recent construction of optimal LRCs-based on cyclic codes, constacyclic LRCs are studied in this letter. Specifically, a family of optimal constacyclic (r, delta)(q)-LRCs with unbounded length and minimum distance delta + 2 epsilon is constructed, where 1 <= epsilon <= left perpendicular (delta/2) right perpendicular. A new optimal cyclic (r, delta)(q)-LRC with unbounded length and minimum distance 2 delta is also presented.