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.

翻译：本文重新审视了用于检测非代数拟阵的若干组合与信息论扩展技术，即Dress-Lovász与Ahlswede-Körner扩展性质。我们提出了这些技术的优化方案以降低其计算复杂度，并由此发现了在9个和10个点上的新非代数拟阵。此外，我们利用Ahlswede-Körner扩展性质，为非代数拟阵端口秘密共享方案的信息率找到了更优的下界。