Binary Codes with Locality for Four Erasures

Abstract

In this paper, codes with locality for four erasures are considered. An upper bound on the rate of codes with locality with sequential recovery from four erasures is derived. The rate bound derived here is field independent. An optimal construction for binary codes meeting this rate bound is also provided. The construction is based on regular graphs of girth $6$ and employs the sequential approach of locally recovering from multiple erasures. An extension of this construction that generates codes which can sequentially recover from five erasures is also presented.

5 pages, 2 figures

References in corpus (9)

• A family of optimal locally recoverable codes
• Repair Locality with Multiple Erasure Tolerance
• Locally Repairable Codes with Multiple Repair Alternatives
• Locally Repairable Codes with Functional Repair and Multiple Erasure Tolerance
• Codes with Locality for Two Erasures
• Some Improvements on Locally Repairable Codes
• Binary Linear Locally Repairable Codes
• Binary Locally Repairable Codes ---Sequential Repair for Multiple Erasures
• Bounds on the Parameters of Locally Recoverable Codes

Cited by in corpus (2)

• A Tight Rate Bound and Matching Construction for Locally Recoverable Codes with Sequential Recovery From Any Number of Multiple Erasures
• Erasure Codes for Distributed Storage: Tight Bounds and Matching Constructions