Optimizing Extension Techniques for Discovering Non-Algebraic Matroids
Combinatorics
2025-12-01 v2 Information Theory
math.IT
Abstract
In this work, we revisit some combinatorial and information-theoretic extension techniques for detecting non-algebraic matroids. These are the Dress-Lov\'asz and Ahlswede-K\"orner extension properties. We provide optimizations of these techniques to reduce their computational complexity, finding new non-algebraic matroids on 9 and 10 points. In addition, we use the Ahlswede-K\"orner extension property to find better lower bounds on the information ratio of secret sharing schemes for ports of non-algebraic matroids.
Keywords
Cite
@article{arxiv.2406.18359,
title = {Optimizing Extension Techniques for Discovering Non-Algebraic Matroids},
author = {Michael Bamiloshin and Oriol Farràs},
journal= {arXiv preprint arXiv:2406.18359},
year = {2025}
}
Comments
Full version