TY - JOUR
T1 - Constructions and Properties of Linear Locally Repairable Codes
AU - Ernvall, Toni
AU - Westerbäck, Thomas
AU - Freij-Hollanti, Ragnar
AU - Hollanti, Camilla
PY - 2016/3
Y1 - 2016/3
N2 - In this paper, locally repairable codes with all-symbol locality are studied. Methods to modify already existing codes are presented. It is also shown that, with high probability, a random matrix with a few extra columns guaranteeing the locality property is a generator matrix for a locally repairable code with a good minimum distance. The proof of the result provides a constructive method to find locally repairable codes. Finally, constructions of three infinite classes of optimal vector-linear locally repairable codes over a small alphabet independent of the code size are given.
AB - In this paper, locally repairable codes with all-symbol locality are studied. Methods to modify already existing codes are presented. It is also shown that, with high probability, a random matrix with a few extra columns guaranteeing the locality property is a generator matrix for a locally repairable code with a good minimum distance. The proof of the result provides a constructive method to find locally repairable codes. Finally, constructions of three infinite classes of optimal vector-linear locally repairable codes over a small alphabet independent of the code size are given.
KW - Codes
KW - data storage systems
KW - DISTRIBUTED STORAGE-SYSTEMS
KW - POINTS
KW - MBR
KW - MSR
UR - http://ieeexplore.ieee.org/xpl/articleDetails.jsp?tp=&arnumber=7366742&source=tocalert&dld=YWFsdG8uZmk
U2 - 10.1109/TIT.2015.2512864
DO - 10.1109/TIT.2015.2512864
M3 - Article
SN - 0018-9448
VL - 62
SP - 1129
EP - 1143
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
IS - 3
ER -