Optimizing extension techniques for discovering non-algebraic matroids

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.