Recovery Algorithms for Linear Batch Codes

2026-05-10

AI Summary

This work addresses the lack of systematic analysis of linear batch codes and their recovery algorithms in existing literature. It establishes, for the first time, a unified framework linking linear batch codes with their recovery algorithms, leveraging tools from combinatorics, coding theory, and graph theory to systematically investigate graph-based batch codes defined over arbitrary bipartite graphs. By introducing several novel recovery algorithms and generalizing prior results, the study clarifies the hierarchical relationships and performance boundaries among different algorithms within the context of linear batch codes. This significantly broadens the applicability of graph-based batch codes and strengthens their theoretical foundation.

Abstract

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.

Problem

• linear batch codes
• recovery algorithms
• batch codes
• order hierarchy
• bipartite graphs

Innovation

• linear batch codes
• recovery algorithms
• bipartite graphs
• order hierarchy
• Almost Affinely Disjoint families