Construction of Locally Repairable Codes with Multiple Localities Based on Encoding Polynomial

Tomoya HAMADA  Hideki YAGI  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E101-A   No.12   pp.2047-2054
Publication Date: 2018/12/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E101.A.2047
Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)
Category: Coding theory and techniques
locally repairable codes,  multiple localities,  locality,  distributed storage system,  error correcting codes,  

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Locally repairable codes, which can repair erased symbols from other symbols, have attracted a good deal of attention in recent years because its local repair property is effective on distributed storage systems. (ru, δu)u∈[s]-locally repairable codes with multiple localities, which are an extension of ordinary locally repairable codes, can repair δu-1 erased symbols simultaneously from a set consisting of at most ru symbols. An upper bound on the minimum distance of these codes and a construction method of optimal codes, attaining this bound with equality, were given by Chen, Hao, and Xia. In this paper, we discuss the parameter restrictions of the existing construction, and we propose explicit constructions of optimal codes with multiple localities with relaxed restrictions based on the encoding polynomial introduced by Tamo and Barg. The proposed construction can design a code whose minimum distance is unrealizable by the existing construction.