Optimizing Extension Techniques for Discovering Non-Algebraic Matroids
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908677263327232 |
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| author | Bamiloshin, Michael Farràs, Oriol |
| author_facet | Bamiloshin, Michael Farràs, Oriol |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_18359 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimizing Extension Techniques for Discovering Non-Algebraic Matroids Bamiloshin, Michael Farràs, Oriol Combinatorics Information Theory 05B35, 94A15, 94A62 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. |
| title | Optimizing Extension Techniques for Discovering Non-Algebraic Matroids |
| topic | Combinatorics Information Theory 05B35, 94A15, 94A62 |
| url | https://arxiv.org/abs/2406.18359 |