Constructions of Binary Optimal Locally Repairable Codes via Intersection Subspaces

2021/05/24 by Wenqin Zhang, Zhang, Wenqin, Deng Tang +3
Computer Science · #Advanced Data Storage Technologies #Caching and Content Delivery #Cellular Automata and Applications #FOS: Computer and information sciences #Information Theory (cs.IT)

paper · pdf · doi:10.48550/arxiv.2105.11271

openalex publication_date 2021/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Locally repairable codes (LRCs), which can recover any symbol of a codeword by reading only a small number of other symbols, have been widely used in real-world distributed storage systems, such as Microsoft Azure Storage and Ceph Storage Cluster. Since binary linear LRCs can significantly reduce coding and decoding complexity, constructions of binary LRCs are of particular interest. The aim of this paper is to construct dimensional optimal binary locally repairable codes with disjoint local repair groups. We introduce how to connect intersection subspaces with binary locally repairable codes and construct dimensional optimal binary linear LRCs with locality 2^b (b≥ 3) and minimum distance d≥ 6 by employing intersection subspaces deduced from the direct sum. This method will sufficiently increase the number of possible repair groups of dimensional optimal LRCs, and thus efficiently expanding the range of the construction parameters while keeping the largest code rates compared with all known binary linear LRCs with minimum distance d≥ 6 and locality 2^b (b≥ 3).

Related

• Optimal binary linear locally repairable codes with disjoint repair groups
• Optimal Quaternary Locally Repairable Codes Attaining the Singleton-like Bound
• Some results on locally repairable codes with minimum distance 7 and locality 2
• Some new constructions of optimal linear codes and alphabet-optimal (r,δ)-locally repairable codes
• Optimal Binary Locally Repairable Codes via Anticodes