Constructions of optimal binary locally recoverable codes via a general construction of linear codes

• Main Authors: Luo, Gaojun, Cao, Xiwang
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2021
• Subjects: Science::Mathematics::Algebra; Engineering::Computer science and engineering::Information systems; Distributed Storage System; Locally Recoverable Code
• Online Access: https://hdl.handle.net/10356/150945
• Institution: Nanyang Technological University

Locally recoverable codes play a crucial role in distributed storage systems. Many studies have only focused on the constructions of optimal locally recoverable codes with regard to the Singleton bound. The aim of this paper is to construct optimal binary locally recoverable codes meeting the alphabetdependent bound. Using a general framework for linear codes associated to a set, we provide a new approach to constructing binary locally recoverable codes with locality 2. We turn the problem of designing optimal binary locally recoverable codes into constructing a suitable set. Several constructions of optimal binary locally recoverable codes are proposed by this new method. Finally, we propose constructions of optimal binary locally recoverable codes with locality 2 and locality parameters $(r,\delta)$ by Griesmer codes.