Recovery Algorithms for Linear Batch Codes
For coding theory researchers, this work offers a structured understanding of recovery algorithms in linear batch codes, though it is incremental as it extends existing concepts.
This paper provides the first systematic investigation of linear batch codes with specific recovery algorithms, introducing and analyzing various types and their hierarchical order. It generalizes known results for graph-based batch codes to arbitrary bipartite graphs.
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.