Batch codes are of potential use for load balancing and private information retrieval in distributed data storage systems. Recently, a special case of batch codes, termed functional batch codes, was proposed in the literature. In functional batch codes, users can query linear combinations of the information symbols, and not only the information symbols themselves, as is the case for standard batch codes. In this work, we consider linear functional batch codes with the additional property that every query is answered by using only a small number of coded symbols. We derive bounds on the minimum length of such codes, and evaluate the results by numerical computations.

翻译：批次码在分布式数据存储系统的负载均衡与私有信息检索中具有潜在应用价值。近期文献提出了一种特殊类型的批次码，称为功能批次码。在功能批次码中，用户不仅可以查询信息符号本身（如标准批次码的情形），还能查询信息符号的线性组合。本文研究具有附加特性的线性功能批次码，其每个查询仅需使用少量编码符号即可完成应答。我们推导了此类码最小长度的理论界，并通过数值计算对结果进行了评估。