Singleton-Type Optimal LRCs with Minimum Distance 3 and 4 from Projective Code

被引：5

作者：

Fu, Qiang ^{[1
]}

Li, Ruihu ^{[1
]}

Guo, Luobin ^{[1
]}

Chen, Gang

机构：

[1] Air Force Engn Univ, Basic Sci, Xian, Peoples R China

来源：

IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES | 2021年 / E104A卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Singleton-type bound; optimal locally repairable codes; projective cap; LOCALLY REPAIRABLE CODES; BINARY;

D O I：

10.1587/transfun.2019EAL2158

中图分类号：

TP3 [计算技术、计算机技术];

学科分类号：

0812 ;

摘要：

Locally repairable codes (LRCs) are implemented in distributed storage systems (DSSs) due to their low repair overhead. The locality of an LRC is the number of nodes in DSSs that participate in the repair of failed nodes, which characterizes the repair cost. An LRC is called optimal if its minimum distance attains the Singleton-type upper bound [1]. In this letter, optimal LRCs are considered. Using the concept of projective code in projective space PG(k, q) and shortening strategy, LRCs with d=3 are proposed. Meantime, derived from an ovoid [q(2) + 1, 4, q(2)](q) code (responding to a maximal (q(2) + 1)-cap in PG(3, q)), optimal LRCs over F-q with d = 4 are constructed.

引用

页码：319 / 323

页数：5

共 22 条

[1] Bierbrauer J., 2017, INTRO CODING THEORY, V2nd
[2] Bose RC, 1947, SANKHYA, V8, P107
[3] THE GEOMETRY OF 2-WEIGHT CODES
CALDERBANK, R
KANTOR, WM
[J]. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 1986, 18 : 97 - 122
[4] On the Locality of Codeword Symbols
Gopalan, Parikshit
Huang, Cheng
Simitci, Huseyin
Yekhanin, Sergey
[J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 2012, 58 (11) : 6925 - 6934
[5] Goparaju S, 2014, IEEE INT SYMP INFO, P676, DOI 10.1109/ISIT.2014.6874918
[6] Hao J, 2017, IEEE INT SYMP INFO, P171, DOI 10.1109/ISIT.2017.8006512
[7] Hao J, 2016, IEEE INT SYMP INFO, P440, DOI 10.1109/ISIT.2016.7541337
[8] Hirschfeld J. W. P., 1979, Projective Geometries Over Finite Fields
[9] Hirschfeld JWP., 1985, FINITE PROJECTIVE SP
[10] Binary Linear Locally Repairable Codes
Huang, Pengfei
Yaakobi, Eitan
Uchikawa, Hironori
Siegel, Paul H.
[J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 2016, 62 (11) : 6268 - 6283

← 1 2 3 →