Explicit MSR Codes with Optimal Access, Optimal Sub-Packetization and Small Field Size for d = k+1, k+2, k+3

04/02/2018
by   Myna Vajha, et al.
0

This paper presents the construction of an explicit, optimal-access, high-rate MSR code for any (n,k,d=k+1,k+2,k+3) parameters over the finite field having sub-packetization α = q^n/q, where q=d-k+1 and Q = O(n). The sub-packetization of the current construction meets the lower bound proven in a recent work by Balaji et al. in BalKum. To our understanding the codes presented in this paper are the first explicit constructions of MSR codes with d<(n-1) having optimal sub-packetization, optimal access and small field size.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
03/18/2023

MSR codes with linear field size and smallest sub-packetization for any number of helper nodes

The sub-packetization ℓ and the field size q are of paramount importance...
research
11/27/2020

A Construction of Maximally Recoverable Codes with Order-Optimal Field Size

We construct maximally recoverable codes (corresponding to partial MDS c...
research
01/24/2019

A Systematic Construction of MDS Codes with Small Sub-packetization Level and Near Optimal Repair Bandwidth

In the literature, all the known high-rate MDS codes with the optimal re...
research
06/12/2018

Erasure Codes for Distributed Storage: Tight Bounds and Matching Constructions

This thesis makes several significant contributions to the theory of bot...
research
05/10/2023

Explicit Information-Debt-Optimal Streaming Codes With Small Memory

For a convolutional code in the presence of a symbol erasure channel, th...
research
04/11/2019

An Explicit Rate-Optimal Streaming Code for Channels with Burst and Arbitrary Erasures

In this paper, we consider transmitting a sequence of messages (a stream...
research
08/30/2023

Random Shortening of Linear Codes and Applications

Random linear codes (RLCs) are well known to have nice combinatorial pro...

Please sign up or login with your details

Forgot password? Click here to reset