Bounds on Codes with Locality and Availability

Abstract

In this paper we investigate bounds on rate and minimum distance of codes with $t$ availability. We present bounds on minimum distance of a code with $t$ availability that are tighter than existing bounds. For bounds on rate of a code with $t$ availability, we restrict ourselves to a sub-class of codes with $t$ availability called codes with strict $t$ availability and derive a tighter rate bound. Codes with strict $t$ availability can be defined as the null space of an $(m\times n)$ parity-check matrix $H$, where each row has weight $(r+1)$ and each column has weight $t$, with intersection between support of any two rows atmost one. We also present two general constructions for codes with $t$ availability.

arXiv commentsubmitted to ISIT 2017

References in corpus (8)

• 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
• Bounds on the Parameters of Locally Recoverable Codes

Cited by in corpus (1)

• Erasure Codes for Distributed Storage: Tight Bounds and Matching Constructions