From fa2611fdd9c5843e6c51ede58aff1ca701595cbb Mon Sep 17 00:00:00 2001 From: VVA2024 Date: Sun, 18 Aug 2024 15:41:53 -0400 Subject: [PATCH] ~ --- .../block/distributed_storage/info_retrieval/batch.yml | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/codes/classical/properties/block/distributed_storage/info_retrieval/batch.yml b/codes/classical/properties/block/distributed_storage/info_retrieval/batch.yml index 31f31c5f3..a841564a4 100644 --- a/codes/classical/properties/block/distributed_storage/info_retrieval/batch.yml +++ b/codes/classical/properties/block/distributed_storage/info_retrieval/batch.yml @@ -17,7 +17,7 @@ description: | If, for any multiset \(i_1, i_2, ..., i_k \in [n]\), there is a partition of buckets into subsets \(S_1, ..., S_k \subset [m]\) such that each \(x_{i_j}\) can be recovered by reading at most one symbol from each bucket in \(S_j\), then the \((n, N, k, m)\) code is a \textit{multiset batch code}. -properties: | +protection: | The Gadget Lemma states that any \((n,N,k,m)\) batch code at \(t=1\) can be transformed into a multiset \((rn,rN,k,m)\) for any positive integer \(r\) \cite{doi:10.1109/TIT.2016.2524007}. Combining two batch codes \(C_1\) and \(C_2\), which are \((n_1,N_1,k_1,m_1)\) and \((n_2,N_2,k_2,m_2)\) batch codes respectively, yields a composite batch code \(C_1\otimes C_2\), which is an \((n_1, m_1N_2, k_1 k_2, m_1 m_2)\) batch code.