On Locality of Some Ternary Linear Codes of Dimension 6

Ruipan YANG  Ruihu LI  Luobin GUO  Qiang FU  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E100-A   No.10   pp.2172-2175
Publication Date: 2017/10/01
Online ISSN: 1745-1337
Type of Manuscript: LETTER
Category: Coding Theory
Keyword: 
locally repairable codes,  ternary linear codes,  generator matrices,  locality,  

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Summary: 
Locally repairable code (LRC) can recover any codeword symbol failure by accessing a small number of other symbols, which can increase the efficiency during the repair process. In a distributed storage system with locally repairable codes, any node failure can be rebuilt by accessing other fixed nodes. It is a promising prospect for the application of LRC. In this paper, some methods of constructing matrices which can generate codes with small locality will be proposed firstly. By analyzing the parameters, we construct the generator matrices of the best-known ternary linear codes of dimension 6, using methods such as shortening, puncturing and expansion. After analyzing the linear dependence of the column vectors in the generator matrices above, we find out the locality of the codes they generate. Many codes with small locality have been found.