On the Optimality of Gabidulin-Based LRCs as Codes with Multiple Local Erasure Correction

Abstract

The Gabidulin-based locally repairable code (LRC) construction by Silberstein et al. is an important example of distance optimal (r,δ)-LRCs. Its distance optimality has been further shown to cover the case of multiple (r,δ)-locality, where the (r,δ)-locality constraints are different among different symbols. However, the optimality only holds under the ordered (r,δ) condition, where the parameters of the multiple (r,δ)-locality satisfy a specific ordering condition. In this letter, we show that Gabidulin-based LRCs are still distance optimal even without the ordered (r,δ) condition.