Optimizing Extension Techniques for Discovering Non-Algebraic Matroids
arXiv:2406.18359 · doi:10.1007/s10801-025-01462-y
Abstract
In this work, we revisit some combinatorial and information-theoretic extension techniques for detecting non-algebraic matroids. These are the Dress-Lovász and Ahlswede-Körner 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-Körner extension property to find better lower bounds on the information ratio of secret sharing schemes for ports of non-algebraic matroids.
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