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

Geonu KIM  Jungwoo LEE  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E102-A   No.9   pp.1326-1329
Publication Date: 2019/09/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E102.A.1326
Type of Manuscript: LETTER
Category: Coding Theory
locally repairable codes,  multiple locality,  local erasure correction,  Gabidulin code,  

Full Text: FreePDF(224.2KB)

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.