The Length of Functional Batch and PIR Codes
Information Theory
2026-03-18 v2 math.IT
Abstract
We consider the problem of computing the minimum length of functional batch and PIR codes of fixed dimension and for a fixed list size, over an arbitrary finite field. We recover, generalize, and refine several results that were previously obtained for binary codes. We present new upper and lower bounds for the minimum length, and discuss the asymptotic behaviour of this parameter. We also compute its value for several parameter sets. The paper also offers insights into the "correct" list size to consider for the Functional Batch Conjecture over non-binary finite fields, and establishes various supporting results.
Keywords
Cite
@article{arxiv.2508.02586,
title = {The Length of Functional Batch and PIR Codes},
author = {Altan B. Kilic and Alberto Ravagnani and Flavio Salizzoni},
journal= {arXiv preprint arXiv:2508.02586},
year = {2026}
}