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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.02001 |
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| _version_ | 1866912257616642048 |
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| author | Baghban, Akram Ghiyasvand, Mehdi |
| author_facet | Baghban, Akram Ghiyasvand, Mehdi |
| contents | This paper develops a new family of locally recoverable codes for distributed storage systems, Sequential Locally Recoverable Codes (SLRCs) constructed to handle multiple erasures in a sequential recovery approach. We propose a new connection between parallel and sequential recovery, which leads to a general construction of q-ary linear codes with information $(r, t_i, δ)$-sequential-locality where each of the $i$-th information symbols is contained in $t_i$ punctured subcodes with length $(r+δ-1)$ and minimum distance $δ$. We prove that such codes are $(r, t)_q$-SLRC ($t \geq δt_i+1$), which implies that they permit sequential recovery for up to $t$ erasures each one by $r$ other code symbols. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_02001 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | New Construction of Locally q-ary Sequential Recoverable Codes: Parity-check Matrix Approach Baghban, Akram Ghiyasvand, Mehdi Information Theory H.1.1 This paper develops a new family of locally recoverable codes for distributed storage systems, Sequential Locally Recoverable Codes (SLRCs) constructed to handle multiple erasures in a sequential recovery approach. We propose a new connection between parallel and sequential recovery, which leads to a general construction of q-ary linear codes with information $(r, t_i, δ)$-sequential-locality where each of the $i$-th information symbols is contained in $t_i$ punctured subcodes with length $(r+δ-1)$ and minimum distance $δ$. We prove that such codes are $(r, t)_q$-SLRC ($t \geq δt_i+1$), which implies that they permit sequential recovery for up to $t$ erasures each one by $r$ other code symbols. |
| title | New Construction of Locally q-ary Sequential Recoverable Codes: Parity-check Matrix Approach |
| topic | Information Theory H.1.1 |
| url | https://arxiv.org/abs/2503.02001 |