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

• HAMADA Tomoya

  Department of Communication Engineering and Informatics, University of Electro-Communications

• YAGI Hideki

  Department of Communication Engineering and Informatics, University of Electro-Communications

抄録

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. (r_u, δ_u)_u∈[s]-locally repairable codes with multiple localities, which are an extension of ordinary locally repairable codes, can repair δ_u-1 erased symbols simultaneously from a set consisting of at most r_u 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.

収録刊行物

• IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

  IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E101.A (12), 2047-2054, 2018-12-01

  一般社団法人 電子情報通信学会

キーワード

• locally repairable codes
• multiple localities
• locality
• distributed storage system
• error correcting codes

詳細情報

• CRID: 1390845713025394560
• NII論文ID: 130007539041
• DOI: 10.1587/transfun.e101.a.2047
• ISSN: 17451337
• ISSN: 09168508
• Web Site: https://www.jstage.jst.go.jp/article/transfun/E101.A/12/E101.A_2047/_pdf
• 本文言語コード: en
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