T-code: 3-erasure longest lowest-density MDS codes

Authors:
Sheng Lin;Gang Wang;Douglas S. Stones;Xiaoguang Liu;Jing Liu
Affiliations:
Nankai-Baidu Joint Lab, College of Information Technical Science, Nankai University, Tianjin, China;Nankai-Baidu Joint Lab, College of Information Technical Science, Nankai University, Tianjin, China;School of Mathematical Sciences, Monash University, VIC, Australia;Nankai-Baidu Joint Lab, College of Information Technical Science, Nankai University, Tianjin, China;Nankai-Baidu Joint Lab, College of Information Technical Science, Nankai University, Tianjin, China
Venue:
IEEE Journal on Selected Areas in Communications
Year:
2010

Citing 12
Cited 0

EVENODD: An Efficient Scheme for Tolerating Double Disk Failures in RAID Architectures

IEEE Transactions on Computers - Special issue on fault-tolerant computing
A tutorial on Reed-Solomon coding for fault-tolerance in RAID-like systems

Software—Practice & Experience
Awarded Best Paper! -- Row-Diagonal Parity for Double Disk Failure Correction

FAST '04 Proceedings of the 3rd USENIX Conference on File and Storage Technologies
HoVer Erasure Codes For Disk Arrays

DSN '06 Proceedings of the International Conference on Dependable Systems and Networks
New families of atomic Latin squares and perfect 1-factorisations

Journal of Combinatorial Theory Series A
Optimizing Cauchy Reed-Solomon Codes for Fault-Tolerant Network Storage Applications

NCA '06 Proceedings of the Fifth IEEE International Symposium on Network Computing and Applications
Handbook of Combinatorial Designs, Second Edition (Discrete Mathematics and Its Applications)

Handbook of Combinatorial Designs, Second Edition (Discrete Mathematics and Its Applications)
MDS array codes with independent parity symbols

IEEE Transactions on Information Theory
On lowest density MDS codes

IEEE Transactions on Information Theory
X-code: MDS array codes with optimal encoding

IEEE Transactions on Information Theory
Low-density MDS codes and factors of complete graphs

IEEE Transactions on Information Theory
Lowest density MDS codes over extension alphabets

IEEE Transactions on Information Theory

Quantified Score

Hi-index	0.07

Visualization

Abstract

In this paper, we study longest lowest-density MDS codes, a simple kind of multi-erasure array code with optimal redundancy and minimum update penalty. We prove some basic structure properties for longest lowest-density MDS codes. We define a "perfect" property for near-resolvable block designs (NRBs) and establish a bijection between 3-erasure longest lowest-density MDS codes (T-Codes) and perfect NRB(3k + 1, 3, 2)s. We present a class of NRB(3k+1, 3, 2)s, and prove that it produces a family of T-Codes. This family is infinite assuming Artin's Conjecture. We also test some other NRBs and find some T-Code instances outside of this family.