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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.