Optimal Functional $2^{s-1}$-Batch Codes: Exploring New Sufficient Conditions
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910794024747008 |
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| author | Yohananov, Lev Essayag, Isaac Barouch |
| author_facet | Yohananov, Lev Essayag, Isaac Barouch |
| contents | A functional $k$-batch code of dimension $s$ consists of $n$ servers storing linear combinations of $s$ linearly independent information bits. These codes are designed to recover any multiset of $k$ requests, each being a linear combination of the information bits, by $k$ disjoint subsets of servers. A recent conjecture suggests that for any set of $k = 2^{s-1}$ requests, the optimal solution requires $2^s-1$ servers. This paper shows that the problem of functional $k$-batch codes is equivalent to several other problems. Using these equivalences, we derive sufficient conditions that improve understanding of the problem and enhance the ability to find the optimal solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_11122 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal Functional $2^{s-1}$-Batch Codes: Exploring New Sufficient Conditions Yohananov, Lev Essayag, Isaac Barouch Information Theory A functional $k$-batch code of dimension $s$ consists of $n$ servers storing linear combinations of $s$ linearly independent information bits. These codes are designed to recover any multiset of $k$ requests, each being a linear combination of the information bits, by $k$ disjoint subsets of servers. A recent conjecture suggests that for any set of $k = 2^{s-1}$ requests, the optimal solution requires $2^s-1$ servers. This paper shows that the problem of functional $k$-batch codes is equivalent to several other problems. Using these equivalences, we derive sufficient conditions that improve understanding of the problem and enhance the ability to find the optimal solution. |
| title | Optimal Functional $2^{s-1}$-Batch Codes: Exploring New Sufficient Conditions |
| topic | Information Theory |
| url | https://arxiv.org/abs/2501.11122 |