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<p>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.</p>

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Optimizing extension techniques for discovering non-algebraic matroids

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年10月30日

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  • Michael Bamiloshin,
  • Oriol Farràs

摘要

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.