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arXiv · 2509.15013

Improved Constructions and Lower Bounds for Maximally Recoverable Grid Codes

Joshua Brakensiek·Manik Dhar·Sivakanth Gopi
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Abstract

In this paper, we continue the study of Maximally Recoverable (MR) Grid Codes initiated by Gopalan et al. [SODA 2017]. More precisely, we study codes over an $m \times n$ grid topology with one parity check per row and column of the grid along with $h \ge 1$ global parity checks. Previous works have largely focused on the setting in which $m = n$, where explicit constructions require field size which is exponential in $n$. Motivated by practical applications, we consider the regime in which $m,h$ are constants and $n$ is growing. In this setting, we provide a number of new explicit constructions whose field size is polynomial in $n$. We further complement these results with new field size lower bounds.

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Joshua Brakensiek, Manik Dhar, Sivakanth Gopi. 2025-09-18. Improved Constructions and Lower Bounds for Maximally Recoverable Grid Codes. https://arxiv.org/abs/2509.15013

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