2025/01/19 by Lev Yohananov, Yohananov, Lev, Isaac Barouch Essayag +1 · 1 citation
Computer Science · #Advanced Data Storage Technologies #Cellular Automata and Applications #Coding theory and cryptography #FOS: Computer and information sciences #Information Theory (cs.IT)
paper · pdf · doi:10.48550/arxiv.2501.11122
openalex publication_date 2025/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 = 2s-1 requests, the optimal solution requires 2s-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.