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arXiv · 2610.28820

A Matroidal Framework for Random Access in Linear Codes

Daniella Bar-Lev·Hiram H. López·Gretchen L. Matthews·Flavio Salizzoni
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Abstract

We study random access in linear codes when codeword symbols are sampled independently and uniformly with replacement. A code is recovery balanced if the expected number of samples required to recover a codeword coordinate is the same for every coordinate. We express the recovery expectations in terms of the associated matroid and derive a coordinatewise identity relating these values for a code and its dual. This proves that a linear code is recovery balanced if and only if its dual is recovery balanced, establishing a conjecture of Gruica et al. We further define the recovery balance for arbitrary matroids and show that asymptotically almost every sparse paving matroid is not recovery balanced.

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Daniella Bar-Lev, Hiram H. López, Gretchen L. Matthews, Flavio Salizzoni. 2026-10-20. A Matroidal Framework for Random Access in Linear Codes. https://arxiv.org/abs/2610.28820

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