Explicit constructions of optimal vector locally repairable codes
摘要
Advanced coding technologies have been proposed to prevent data loss caused by node failures in distributed storage systems. Locally repairable code (LRC) is an important distributed storage codes. This paper focuses on optimal vector LRC, where a vector LRC is optimal if the code distance attains the existing bound with equality. In this paper, an optimal vector LRC that can reduce repair bandwidth is proposed for the first time. This code achieves minimum repair access and has a simple repair property, where an optimal vector LRC is called having minimum repair access if both repair bandwidth and repair access achieve the existing bound with equality, and a vector LRC with simple repair property refers to vector LRC that only uses the XOR operation in repair. In addition, an optimal vector LRC with simple repair property under a new class of parameters is provided. These codes are constructed using Reed-Solomon encoded blocks and can achieve arbitrary high code rate.