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arXiv · 2601.16628

The Oval Strikes Back

Andrea Di Giusto·Alberto Ravagnani·Emina Soljanin
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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.

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Andrea Di Giusto, Alberto Ravagnani, Emina Soljanin. 2026-01-23. The Oval Strikes Back. https://arxiv.org/abs/2601.16628

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