A Bound on the Minimal Field Size of LRCs, and Cyclic MR Codes That Attain It

Han Cai; Moshe Schwartz

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A Bound on the Minimal Field Size of LRCs, and Cyclic MR Codes That Attain It

机译：A Bound on the Minimal Field Size of LRCs, and Cyclic MR Codes That Attain It

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摘要

We prove a new lower bound on the field size of locally repairable codes (LRCs). Additionally, we construct maximally recoverable (MR) codes which are cyclic. While a known construction for MR codes has the same parameters, it produces non-cyclic codes. Furthermore, we prove both necessary conditions and sufficient conditions that specify when the known non-cyclic MR codes may be permuted to become cyclic, thus proving our construction produces cyclic MR codes with new parameters. Furthermore, using our new bound on the field size, we show that the new cyclic MR codes have optimal field size in certain cases. Other known LRCs are also shown to have optimal field size in certain cases.

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来源
《IEEE Transactions on Information Theory》 |2023年第4期|2240-2260|共21页
作者
Han Cai; Moshe Schwartz;
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作者单位

School of Information Science and Technology, Southwest Jiaotong University, Chengdu, China;

School of Electrical and Computer Engineering, Ben-Gurion University of the Negev, Beer Sheva, Israel;

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正文语种英语
中图分类通信;
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Codes; Symbols; Maintenance engineering; Hamming distances; Linear codes; Codecs; Generators;

A Bound on the Minimal Field Size of LRCs, and Cyclic MR Codes That Attain It

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