Improved Upper Bounds for the Information Rates of the Secret Sharing Schemes Induced by the Vamos Matroid

英文摘要：

An access structure specifying the qualified sets of a secret sharing scheme must have information rate less than or equal to one. The Vamos matroid induces two non-isomorphic access structures V1 and V6, which were shown by Marti-Farre and Padro to have information rates of at least 3/4. Beimel, Livne, and Padro showed that the information rates of V1 and V6 are bounded above by 10/11 and 9/10 respectively. Here we improve those upper bounds to 19/21 for V1 and 17/19 for V6.