How to Find New Characteristic-Dependent Linear Rank Inequalities using Secret Sharing

Abstract: Determining information ratios of access structures is an important problem in secret sharing. Information inequalities and linear rank inequalities play an important role for proving bounds. Characteristic-dependent linear rank inequalities are rank inequalities which are true over vector spaces with specific field characteristic. In this paper, using ideas of secret sharing, we show a theorem that produces characteristic-dependent linear rank inequalities. These inequalities can be used for getting lower bounds on information ratios in linear secret sharing.