Optimizing Extension Techniques for Discovering Non-Algebraic Matroids
<|reference_start|>Optimizing Extension Techniques for Discovering Non-Algebraic Matroids: 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.<|reference_end|>
@article{bamiloshin2024optimizing,
    title={Optimizing Extension Techniques for Discovering Non-Algebraic Matroids},
    author={Michael Bamiloshin and Oriol Farr`as},
    journal={arXiv preprint arXiv:2406.18359},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.18359},
    primaryClass={math.CO cs.IT math.IT}
}