Optimal Locally Repairable Codes: An Improved Bound and Constructions

We study the Singleton-type bound that provides an upper limit on the minimum distance of locally repairable codes. We present an improved bound by carefully analyzing the combinatorial structure of the repair sets. Thus, we show the previous bound is unachievable for certain parameters. We then als...

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Bibliographic Details
Published inIEEE transactions on information theory Vol. 68; no. 8; pp. 5060 - 5074
Main Authors Cai, Han, Fan, Cuiling, Miao, Ying, Schwartz, Moshe, Tang, Xiaohu
Format Journal Article
LanguageEnglish
Published New York IEEE 01.08.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Codes
Combinatorial analysis
Fans
Generators
Hamming distance
Linear codes
Locally repairable codes
Maintenance engineering
Parameters
Singleton-type bound
Upper bound
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Summary:We study the Singleton-type bound that provides an upper limit on the minimum distance of locally repairable codes. We present an improved bound by carefully analyzing the combinatorial structure of the repair sets. Thus, we show the previous bound is unachievable for certain parameters. We then also provide explicit constructions of optimal codes which show that for certain parameters the new bound is sharp. Additionally, as a byproduct, some previously known codes are shown to attain the new bound and are thus proved to be optimal.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2022.3161613