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arXiv · 2310.00467

New results on Erasure Combinatorial Batch Codes

Phuc-Lu Le·Son Hoang Dau·Hy Dinh Ngo·Thuc D. Nguyen
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Abstract

We investigate in this work the problem of Erasure Combinatorial Batch Codes, in which $n$ files are stored on $m$ servers so that every set of $n-r$ servers allows a client to retrieve at most $k$ distinct files by downloading at most $t$ files from each server. Previous studies have solved this problem for the special case of $t=1$ using Combinatorial Batch Codes. We tackle the general case $t \geq 1$ using a generalization of Hall's theorem. Additionally, we address a realistic scenario in which the retrieved files are consecutive according to some order and provide a simple and optimal solution for this case.

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Phuc-Lu Le, Son Hoang Dau, Hy Dinh Ngo, Thuc D. Nguyen. 2023-09-30. New results on Erasure Combinatorial Batch Codes. https://arxiv.org/abs/2310.00467

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