论文标题
线性编程中的对称性，以获取信息不平等的信息
Symmetries in Linear Programming for Information Inequalities
论文作者
论文摘要
我们研究了秘密共享计划的属性，其中将随机的秘密价值转化为在几个参与者中分布的股票，以使只有合格的参与者可以恢复秘密价值的方式。对于几个特定的秘密共享问题，我们改善了股票量的低界限。为此，我们使用了非香农型信息不等式的方法，可以追溯到Z. Zhang和R.W. Yeung。我们采用并扩展了线性编程技术，该技术允许间接应用新信息不平等，甚至无明确地写下它们。为了减少范围中涉及的线性编程问题的复杂性，我们广泛使用对称性考虑。
We study the properties of secret sharing schemes, where a random secret value is transformed into shares distributed among several participants in such a way that only the qualified groups of participants can recover the secret value. We improve the lower bounds on the sizes of shares for several specific problems of secret sharing. To this end, we use the method of non-Shannon-type information inequalities going back to Z. Zhang and R.W. Yeung. We employ and extend the linear programming technique that allows to apply new information inequalities indirectly, without even writing them down explicitly. To reduce the complexity of the problems of linear programming involved in the bounds we extensively use symmetry considerations.
