Girth-Based Sequential-Recovery LRCs
In this paper, we prove that a linear block code with girth <inline-formula> <tex-math notation="LaTeX">$2(t+1)$ </tex-math></inline-formula> is a <inline-formula> <tex-math notation="LaTeX">$t$ </tex-math></inline-formula>-sequenti...
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| Format: | Article |
| Language: | English |
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IEEE
2022-01-01
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| Series: | IEEE Access |
| Subjects: | |
| Online Access: | https://ieeexplore.ieee.org/document/9968006/ |
| _version_ | 1811178313592340480 |
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| author | Zhi Jing Hong-Yeop Song |
| author_facet | Zhi Jing Hong-Yeop Song |
| author_sort | Zhi Jing |
| collection | DOAJ |
| description | In this paper, we prove that a linear block code with girth <inline-formula> <tex-math notation="LaTeX">$2(t+1)$ </tex-math></inline-formula> is a <inline-formula> <tex-math notation="LaTeX">$t$ </tex-math></inline-formula>-sequential-recovery locally repairable codes (LRCs) with locality <inline-formula> <tex-math notation="LaTeX">$r$ </tex-math></inline-formula> if its parity-check matrix has column weight at least 2 and row weight at most <inline-formula> <tex-math notation="LaTeX">$r+1$ </tex-math></inline-formula>. This gives a new connection between sequential-recovery LRCs and linear block codes. We also derive that the repair time of the <inline-formula> <tex-math notation="LaTeX">$t$ </tex-math></inline-formula>-sequential-recovery LRCs from the linear block codes by this connection is at most <inline-formula> <tex-math notation="LaTeX">$\lceil t/2 \rceil $ </tex-math></inline-formula>. |
| first_indexed | 2024-04-11T06:17:34Z |
| format | Article |
| id | doaj.art-8452cf445d8745548a72c50d3d51b032 |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-04-11T06:17:34Z |
| publishDate | 2022-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-8452cf445d8745548a72c50d3d51b0322022-12-22T04:41:01ZengIEEEIEEE Access2169-35362022-01-011012615612616010.1109/ACCESS.2022.32259059968006Girth-Based Sequential-Recovery LRCsZhi Jing0https://orcid.org/0000-0002-1444-3289Hong-Yeop Song1https://orcid.org/0000-0001-8764-9424School of Electrical and Electronic Engineering, Yonsei University, Seoul, South KoreaSchool of Electrical and Electronic Engineering, Yonsei University, Seoul, South KoreaIn this paper, we prove that a linear block code with girth <inline-formula> <tex-math notation="LaTeX">$2(t+1)$ </tex-math></inline-formula> is a <inline-formula> <tex-math notation="LaTeX">$t$ </tex-math></inline-formula>-sequential-recovery locally repairable codes (LRCs) with locality <inline-formula> <tex-math notation="LaTeX">$r$ </tex-math></inline-formula> if its parity-check matrix has column weight at least 2 and row weight at most <inline-formula> <tex-math notation="LaTeX">$r+1$ </tex-math></inline-formula>. This gives a new connection between sequential-recovery LRCs and linear block codes. We also derive that the repair time of the <inline-formula> <tex-math notation="LaTeX">$t$ </tex-math></inline-formula>-sequential-recovery LRCs from the linear block codes by this connection is at most <inline-formula> <tex-math notation="LaTeX">$\lceil t/2 \rceil $ </tex-math></inline-formula>.https://ieeexplore.ieee.org/document/9968006/Locally repairable codesjoint sequential-parallel-recoverygirthrepair time |
| spellingShingle | Zhi Jing Hong-Yeop Song Girth-Based Sequential-Recovery LRCs IEEE Access Locally repairable codes joint sequential-parallel-recovery girth repair time |
| title | Girth-Based Sequential-Recovery LRCs |
| title_full | Girth-Based Sequential-Recovery LRCs |
| title_fullStr | Girth-Based Sequential-Recovery LRCs |
| title_full_unstemmed | Girth-Based Sequential-Recovery LRCs |
| title_short | Girth-Based Sequential-Recovery LRCs |
| title_sort | girth based sequential recovery lrcs |
| topic | Locally repairable codes joint sequential-parallel-recovery girth repair time |
| url | https://ieeexplore.ieee.org/document/9968006/ |
| work_keys_str_mv | AT zhijing girthbasedsequentialrecoverylrcs AT hongyeopsong girthbasedsequentialrecoverylrcs |