Abstract:

In order to enhance the precision of the minimum distance and narrow its scope, this paper proposes two new bounds on the minimum distance which apply to Locally Repairable Codes. First, one bound is proposed by theoretical derivation on the basis of the Singleton-like bound. Second, the other is proposed based on existing methods and the new one proposed, and it is smaller in scope. Third, the connections are proposed among minimum distance bounds. Finally, simulation results show that the first new proposed bound is no better than the Singleton-like bound and the other is better than existing bounds on the minimum distance. 

Key words: locally repairable codes, minimum distance, distributed storage systems, erasure codes