Secret-Sharing Matroids need not be Algebraic
arXiv:1403.6363 · doi:10.1016/j.disc.2016.02.012
Abstract
We combine some known results and techniques with new ones to show that there exists a non-algebraic, multi-linear matroid. This answers an open question by Matus (Discrete Mathematics 1999), and an open question by Pendavingh and van Zwam (Advances in Applied Mathematics 2013). The proof is constructive and the matroid is explicitly given.