Optimal Binary Locally Repairable Codes via Anticodes

Abstract

This paper presents a construction for several families of optimal binary locally repairable codes (LRCs) with small locality (2 and 3). This construction is based on various anticodes. It provides binary LRCs which attain the Cadambe-Mazumdar bound. Moreover, most of these codes are optimal with respect to the Griesmer bound.

References in corpus (5)

• A family of optimal locally recoverable codes
• Locally Repairable Codes with Multiple Repair Alternatives
• Binary Cyclic Codes that are Locally Repairable
• Codes and Designs Related to Lifted MRD Codes
• Explicit MBR All-Symbol Locality Codes

Cited by in corpus (6)

• Optimal binary linear locally repairable codes with disjoint repair groups
• Erasure Coding for Distributed Storage: An Overview
• Constructions of Optimal Cyclic $(r,\delta )$ Locally Repairable Codes
• Bounds and Constructions for Linear Locally Repairable Codes over Binary Fields
• On the Average Locality of Locally Repairable Codes
• Locality and Availability of Array Codes Constructed from Subspaces