Explicit Constructions and Bounds for Batch Codes with Restricted Size of Reconstruction Sets

TL;DR

This paper investigates linear batch and PIR codes with restricted reconstruction set sizes, deriving new bounds and constructions for small parameters, extending previous theoretical frameworks.

Contribution

It introduces new bounds and explicit constructions for batch and PIR codes with limited reconstruction set sizes, building on prior recursive bounds.

Findings

New bounds for small t and r parameters

Explicit constructions matching bounds

Extension of Cadambe and Mazumdar's recursive bounds

Abstract

Linear batch codes and codes for private information retrieval (PIR) with a query size $t$ and a restricted size $r$ of the reconstruction sets are studied. New bounds on the parameters of such codes are derived for small values of $t$ or of $r$ by providing corresponding constructions. By building on the ideas of Cadambe and Mazumdar, a new bound in a recursive form is derived for batch codes and PIR codes.