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On generalized combinatorial batch codes
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DOI：10.1016/j.dam.2026.04.038.png)
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Abstract
En 中文
Combinatorial batch codes were defined by Paterson et al. (2009) as a purely combinatorial version of batch codes introduced by Ishai et al. (2004). There are n items and m servers each of which stores a subset of the items such that any k distinct items can be retrieved by reading at most t elements from each server. To address server failures and parallel multiple users retrieval issues in complex scenarios, we propose a generalization of combinatorial batch codes, named generalized combinatorial batch codes (GCBC), in which n items are stored in m servers, such that any multiset request of k items, where any item is requested at most s times, can be retrieved by reading at most t items from each server, while any r servers are unavailable (failed). In this paper, we provide necessary and sufficient conditions for the existence of GCBCs based on incidence matrices and extended Hall's conditions. By this we determine the optimal (minimum) total storage of GCBCs with t = 1 for extreme values of n and other special parameter sets, including m = r + k and r = 1, s = 2, and present several constructions of GCBCs. (c) 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
Keywords:
Combinatorial batch code
Hall's condition
Optimal value
Journal
D
IF:
1.1
Papers:
336
Citations:
7.7K