# Constructions of Batch Codes via Finite Geometry

## TL;DR

This paper introduces new explicit and random linear primitive batch codes constructed using finite geometry, achieving lower redundancy in certain parameter regimes compared to existing codes.

## Contribution

It presents novel finite geometry-based constructions of linear primitive batch codes, improving redundancy efficiency over prior methods.

## Key findings

- Codes have lower redundancy in some parameter regimes.
- Explicit and random constructions are developed.
- Linear primitive batch codes are successfully constructed.

## Abstract

A primitive $k$-batch code encodes a string $x$ of length $n$ into string $y$ of length $N$, such that each multiset of $k$ symbols from $x$ has $k$ mutually disjoint recovering sets from $y$. We develop new explicit and random coding constructions of linear primitive batch codes based on finite geometry. In some parameter regimes, our proposed codes have lower redundancy than previously known batch codes.