The Oval Strikes Back
Abstract
We investigate the applications of ovals in projective planes to distributed storage, with a focus on the Service Rate Region problem. Leveraging the incidence relations between lines and ovals, we describe a class of non-systematic MDS matrices with a large number of small and disjoint recovery sets. For certain parameter choices, the service-rate region of these matrices contains the region of a systematic generator matrix for the same code, yielding better service performance. We further apply our construction to analyze the PIR properties of the considered MDS matrices and present a one-step majority-logic decoding algorithm with strong error-correcting capability. These results highlight how ovals, a classical object in finite geometry, re-emerge as a useful tool in modern coding theory.
Cite
@article{arxiv.2601.16628,
title = {The Oval Strikes Back},
author = {Andrea Di Giusto and Alberto Ravagnani and Emina Soljanin},
journal= {arXiv preprint arXiv:2601.16628},
year = {2026}
}