Various types of recovery algorithms for batch codes have been investigated, such as asynchronous recovery or recovery as afforded by batch codes obtained from Almost Affinely Disjoint (AAD) families. In this paper, we offer the first systematic investigation of linear batch codes equipped with particular recovery algorithms. We introduce and investigate various known and new types of algorithms, and we investigate the order hierarchy of these types of batch codes. The simplest known recovery algorithms are those associated with graph-based batch codes. We investigate the resulting batch codes for arbitrary bipartite graphs, thereby generalizing some known results.

翻译：针对批处理码的各类恢复算法已有研究，例如异步恢复或通过近似仿射不交（AAD）族构建的批处理码所提供的恢复机制。本文首次系统研究了配备特定恢复算法的线性批处理码。我们引入并分析了多种已知及新型算法类型，并探讨了这些批处理码类型的序关系层级。最简单的已知恢复算法与基于图的批处理码相关。我们研究了任意二分图对应的批处理码，从而推广了若干已知结论。