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A weighted module view of integral closures of affine domains of type I
Combinatorial batch codes
| 1. | Department of Mathematics, Royal Holloway, University of London, Egham, Surrey TW20 0EX, United Kingdom |
| 2. | David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, ON, N2L 3G1, Canada |
| 3. | Department of Computer Science, Lakehead University, hunder Bay, ON, P7B 5E1, Canada |
We restrict out attention to batch codes in which every server stores a subset of the items. This is purely a combinatorial problem, so we call this kind of batch code a ''combinatorial batch code''. We only study the special case $t=1$, where, for various parameter situations, we are able to present batch codes that are optimal with respect to the storage requirement, $N$. We also study uniform codes, where every item is stored in precisely $c$ of the $m$ servers (such a code is said to have rate $1/c$). Interesting new results are presented in the cases $c = 2, k-2$ and $k-1$. In addition, we obtain improved existence results for arbitrary fixed $c$ using the probabilistic method.
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