PreprintCC BY 4.0arXiv
A Matroidal Framework for Random Access in Linear Codes
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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BibTeX
@misc{barlev2026matroidal,
title = {{A Matroidal Framework for Random Access in Linear Codes}},
author = {Daniella Bar-Lev and Hiram H. López and Gretchen L. Matthews and Flavio Salizzoni},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.28820},
eprint = {2610.28820},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.28820},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Matroidal Framework for Random Access in Linear Codes
AU - Daniella Bar-Lev
AU - Hiram H. López
AU - Gretchen L. Matthews
AU - Flavio Salizzoni
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.28820
UR - https://arxiv.org/abs/2610.28820
AB - 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.
ER -